Capturing the Impact of Riverine Nutrient Delivery on Coastal Ocean Biogeochemistry · 2018. 10. 10. · 1 Abstract Capturing the Impact of Riverine Nutrient Delivery on Coastal Ocean

Capturing the Impact of Riverine Nutrient Delivery on Coastal Ocean Biogeochemistry

By

Elizabeth Halley Olhsson

A dissertation submitted in partial satisfaction of the

requirements for the degree of

Doctor of Philosophy

in

Environmental Science, Policy and Management

in the

Graduate Division

of the

University of California, Berkeley

Committee in charge:

Professor Thomas M. Powell, co-Chair

Professor Wayne Getz, co-Chair

Professor Dennis Baldocchi

Professor William Dietrich

Fall 2014

1

Abstract

Capturing the Impact of Riverine Nutrient Delivery on Coastal Ocean Biogeochemistry

by

Elizabeth Halley Olhsson

Doctor of Philosophy in Environmental Science, Policy and Management

University of California, Berkeley

Professor Thomas M. Powell, co-Chair

Professor Wayne Getz, co-Chair

Rivers smaller than the Amazon tend to be excluded from earth system modeling efforts. Does it

matter? Do sub-grid-scale rivers have significant impacts on offshore primary productivity?

Using the Eel River in northern California, the river with the largest sediment yield per drainage

area in the continental United States, as a test case, this question is explored using two

approaches. First, a data-driven analysis of relevant time series taken on land, by buoy, and from

space, demonstrates very little evidence of direct impact of Eel River discharge on

contemporaneous coastal ocean primary productivity – but to the extent that that evidence exists,

it seems to occur during years of greatest river discharge. To further analyze mechanistic

drivers, a coupled mesoscale modeling framework unifying ocean, watershed and atmospheric

representations is formulated and run in hindcast over the 2002-2010 period. Monthly average

climatologies, interannual variabilities, and event-driven analysis of each year’s largest river

discharge are all examined for evidence of a river-ocean connection expressed through primary

production. Storm event-generated turbulence appears to dominate the primary productivity

during the winter months. The impact of the river seems to be largely independent of nutrient

load, because its dissolved nitrate is less than that of the coastal ocean. There is no evidence that

riverine delivery of gradually bioavailable detritus has a significant effect. Although a

sufficiently super-nitrous river shows the ability to sustain a plume-nutrient-driven-bloom even

at periods of extremely low flow, this is not currently a realistic scenario for the Eel River. The

possibility remains that another micronutrient not studied in the modeling framework, such as

iron, could be important to this system.

i

Dedication

For Gary, my dad.

ii

Table of Contents

Abstract 1

Dedication i

Table of Contents ii

List of Figures v

List of Tables x

Introduction xii

Acknowledgements xv

Chapter 1: Eel River Data Analysis

1.1 Introduction 1

1.2 The Eel River: Overview 1

1.3 The Eel River: Literature Review 3

1.3.1 1910-1979 3

1.3.2 1980-1989 4

1.3.3 1990-1999 4

1.3.4 2000-present 6

1.3.5 Empirical Sediment Models and the Eel 7

1.4 Data Analysis: Overview 9

1.5 Estimation of NPP from ocean color data 11

1.6 MODIS data 12

1.7 NBDC buoy data 13

1.8 USGS gauging station data 14

1.9 Methodology: Granger’s Test for Predictive Causality 14

1.10 Results: Granger Causality 15

1.11 Methodology: Canonical Correlation Analysis 18

1.12 Results: CCA 20

1.13 Discussion and Conclusion 22

Chapter 2: Methodology

2.1 Introduction and Literature Review: Previous Relevant Modeling Efforts 34

2.2 Modeling Framework Overview 36

2.3 Atmospheric Forcing 37

2.3.1 NARR 38

2.3.2 Bulk flux approximations in ROMS, 10 km horizontal resolution 38

2.3.3 ERA-Interim 38

2.3.4 Comparison: ERA-Interim vs. NARR, regional scale 39

2.3.5 Comparison: ERA-Interim vs. NARR vs. Daymet data, local scale 49

2.4 Hydrological Modeling: HydroTrend 54

2.4.1 HydroTrend Description 54

2.4.2 HydroTrend Discharge 55

2.4.3 HydroTrend Sediment 58

2.4.4 HydroTrend Parameterization 60

2.5 Ocean Modeling: Regional Ocean Modeling System 63

iii

2.5.1 Equations of Motion 63

2.5.2 Curvilinear Coordinates 65

2.5.3 Vertical Coordinates 65

2.5.4 Domain and Grid Resolution 66

2.5.5 Bathymetry 68

2.5.6 Temporal Resolution and Numerics 69

2.5.7 Horizontal Diffusion and Viscosity 70

2.5.8 Vertical Mixing Parameterization 70

2.5.9 Boundary Conditions 71

2.5.9.1 Lateral Boundary Conditions 71

2.5.9.2 Bottom Boundary Conditions 72

2.5.10 Surface Model Forcing 73

2.5.11 River Forcing 74

2.5.12 Model Initialization and Spinup 75

2.6 Biogeochemical Modeling: Nutrient-Phytoplankton-Zooplankton-Detritus 76

2.6.1 NPZD description and limitations 76

2.6.2 NPZD ROMS dynamics 79

2.6.3 NPZD initial and boundary conditions 79

2.6.4 NPZD riverine input 79

2.7 Model Experimental Design 83

2.8 Model Results 84

2.8.1 Results: HydroTrend 84

2.8.2 Results: ROMS, 10 km resolution 87

2.8.2.1 Climatological validation 87

2.8.2.2 Short timescale validation 91

2.8.3 Results: ROMS, 1 km resolution 93

2.9 Conclusion 95

Chapter 3: Results

3.1 Introduction 96

3.2 MODIS validation; coverage and cloud gap-filling 98

3.3 Climatological comparisons 102

3.4 Interannual variability comparisons 106

3.4.1 Correlative analysis of December 2002-2009 106

3.4.2 Empirical Orthogonal Function analysis of December Interannual Variability 110

3.4.3 Comparison of Decembers with varying river conditions 113

3.4.4 Summary of interannual variability comparisons 122

3.5 Event-driven comparisons 124

3.5.1 Large river, deep mixed layer 126

3.5.2 Small river, deep mixed layer 128

3.5.3 Large river, shallow mixed layer 130

3.5.4 Small river, shallow mixed layer 132

3.5.5 Summary of event-driven comparisons 134

3.6 No-nutrient river modeling 134

3.7 Extra-nutrient river modeling 138

3.8 Chl:C sensitivity testing 140

iv

3.9 Southwestern model artifact and nonlinear model drift 140

3.10 Discussion 142

3.11 Future Directions 145

3.12 Conclusion 146

Bibliography 147

v

List of Figures

Figure 1.1: The Eel River watershed (Lisle 1990). 3

Figure 1.2: The NPP (blue left Y axis) and Wind (red, right Y axis) Indices, 2003-

2012.

10

Figure 1.3: Yearly NPP and Wind Index plots, with upwelling and significant months

of river flow shaded.

11

Figure 1.4: Simplified visualization of where satellite data are selected for analysis. 13

Figure 1.5: Granger causality test results, Wind and NPP Indices during the upwelling-

dominated period.

17

Figure 1.6: Granger causality test results, Wind and NPP Indices during the storm-

dominated period.

18

Figure 1.7: The matrix F to be decomposed into EOFs, mapped to have each row as

one year’s worth of time series, and each column a time series of observations for a

given date within a year. Figure adapted from (Bjornsson and Venegas 1997).

19

Figure 1.8: The first and largest modes of covariation (EOF1) for NPP (A) and Wind

(B) in the case where we analyze the system without removing the interannual mean

from each point, and for NPP (C) and Wind (D) when we study the covariance of the

anomalies. The x-axis is day of year. With the upwelling signal (seen in A and B)

removed, other patterns (seen in C and D) emerge to represent most of the covariation.

21

Figure 1.9: The fifth modes of covariation (EOF5) for NPP (A) and Wind (B) in the

case where we analyze the system by removing the interannual mean/seasonality from

each point. The x-axis is day of year. C plots the expansion coefficients/time

amplitudes for A, with the x-axis now showing the 1-7 years of the analysis (2003-

2009). D shows water year river discharge for each of the same years.

22

Figure 1.10: A reference volume of mixed layer in the ocean. �⃑⃑� 1 is the horizontal

velocity of Ekman transport offshore, �⃑⃑� 2 is the upwelling velocity, �⃑� is the surface

wind stress, L is a reference length of coastline, D is the distance offshore, and H is

the depth of the mixed layer.

24

Figure 2.1: The coupled modeling framework. 37

Figure 2.2: 1985-2010 January climatology of precipitation, ERA-Interim subtracted

from NARR, and a histogram of the values that went into the climatologies.

41

Figure 2.3: 1985-2010 July climatology of precipitation, ERA-Interim subtracted from

NARR, and . a histogram of the values that went into the climatologies

42

Figure 2.4: 1985-2010 January climatology of temperature, ERA-Interim subtracted

from NARR, and . a histogram of the values that went into the climatologies

43

Figure 2.5: 1985-2010 July climatology of temperature, ERA-Interim subtracted from

NARR, and . a histogram of the values that went into the climatologies

44

Figure 2.6: 1985-2010 January climatology of U (east-west) winds, ERA-Interim

subtracted from NARR, and . a histogram of the values that went into the climatologies

45

Figure 2.7: 1985-2010 July climatology of U (east-west) winds, ERA-Interim


46

vi

Figure 2.8: 1985-2010 January climatology of V (north-south) winds, ERA-Interim


47

Figure 2.9: 1985-2010 July climatology of V (north-south) winds, ERA-Interim


48

Figures 2.10 (top) and 2.11 (bottom): mean monthly temperature and precipitation for

the Daymet Dataset, the North American Regional Reanalysis, and ERA-Interim.

50

Figure 2.12: Comparison of the within-month standard deviation of Daymet

temperature data to the monthly average difference between Daymet data and the

North American Regional Reanalysis.

51


precipitation data to the monthly average difference between Daymet data and the

North American Regional Reanalysis.

52


temperature data to the monthly average difference between the Daymet data and the

ERA-Interim.

53


precipitation data to the monthly average difference between the Daymet data and the

ERA-Interim.

54

Figure 2.16: Partitioning and transport within the water cycle, in HydroTrend 3.0. 55

Figure 2.17: The spatial extent of the two ROMS domains. 67

Figure 2.18: A graphical representation of the terrain-following vertical structure of

the grid, taken across a vertical transect from eastern to western boundary. The x-axis

is longitude. Note that the long flat stretch to the west is land, and masked off from

the simulation.

68

Figure 2.19 (from Banas 2009b): The structure of an NPZD-type ecosystem model. 78

Figure 2.20: Figure by Dr. Jonah Piovia-Scott. USGS nutrient concentrations at

Scotia, CA taken between 1959-present, and monthly climatological averages.

80

Figure 2.21: Figure by Dr. Jonah Piovia-Scott. USGS nutrient flux at Scotia, CA

calculated by multiplying nutrient concentration at time of measurement by measured

river discharge at time of measurement, and monthly climatological averages. The

flux is clearly dominated by the increased river discharge in the winter.

81

Figure 2.22: A graphical representation of the transformation of HydroTrend output

into NPZD nutrients.

82

Figure 2.23: Annual average discharge vs. sediment load for HydroTrend results

versus the USGS validation data. Note that this is a fairly tight cluster far from zero,

but zoomed in on both axes in order to be able to see the differences.

85

Figure 2.24a: ERA-Interim driven HydroTrend vs. USGS gauging data for discharge,

1998-2010.

86

Figure 2.24b: HydroTrend results vs. USGS data, 1998-2010. 87

Figure 2.25: ROMS 10 km results (left) and SODA (right) for sea surface temperature,

zonal (east-west) velocity and meridional (north-south) velocity climatologies for the

month of January, 2000-2010.

89

Figure 2.26: ROMS 10 km results (left) and SODA (right) for sea surface temperature,

zonal (east-west) velocity and meridional (north-south) velocity climatologies for the

month of July, 2000-2010.

90

vii

Figure 2.27: ROMS vs. satellite sea surface temperature for a 48-hour period around

6/22/2001. The mouth of the Eel River is starred.

91

Figure 2.28: Taylor Diagram for 10 km ROMS results from section 2.8.2. 92

Figure 2.29: 1 km ROMS in the coupled modeling framework, producing a river

plume on 12/24/2004. Units are psu. The bottom plot is the same as the top with the

colorbar zoomed in.

94

Figure 3.1: Daily averaged values of phytoplankton concentration in the first week of

December 2004, taken at 40.5 N, -124.5 W, at the sea surface and at 10m depth.

100

Figure 3.2: Daily averaged values of phytoplankton concentration in the first week of

July 2004, taken at 40.5 N, -124.5 W, at the sea surface and at 10m depth.

101

Figure 3.3: ROMS chlorophyll climatologies (A, D, G), MODIS chlorophyll

climatologies (B, E, H), and the ROMS climatology integrated vertically across the

water column, for water years 2002-2010, with the no-river model control subtracted

(C, F, I). Monthly climatologies are sorted by row for November (top), December

(middle) and January (bottom). Units are mg chl-a per cubic meter (square meter, in

the case of the integration).

104

Figure 3.4: ROMS chlorophyll climatologies (A, D, G), MODIS chlorophyll

climatologies (B, E, H), and the ROMS climatology integrated vertically across the

water column, for water years 2002-2010, with the no-river model control subtracted

(C, F, I). Monthly climatologies are sorted by row for February (top), March (middle)

and April (bottom). Units are mg chl-a per cubic meter (square meter, in the case of

the integration).

105

Figure 3.5: ROMS chlorophyll climatology (A), MODIS chlorophyll climatology (B),

and the ROMS climatology integrated vertically across the water column, for water

years 2002-2010, with the no-river model control subtracted (C). Climatologies are

for the month of May, the latest month in which significant Eel river discharge is

found to ever occur from 2000-2010. Units are mg chl-a per cubic meter (square

meter, in the case of the integration).

106

Figure 3.6: Correlations between mixed layer depth and A: surface stress, B: mean

river discharge, C: shortwave radiation, and E: phytoplankton concentration, as well as

phytoplankton concentration vs. D: mean river discharge and F: shortwave radiation

flux.

109

Figure 3.7: The first three empirical orthogonal functions of the 32-point time series

comprised of four 8-day averages per December from 2002-2009, and their variation

in time of amplitude.

111

Figure 3.8: 8-day averaged time series of Eel River discharge (A), annual Oceanic

Nino Index (B) and Pacific Decadal Oscillation (C) for December 2002-2009. Red

and blue bars are positive and negative anomalies respectively.

112

Figure 3.9: Daily mean Eel River discharge for December 2003, 2005 and 2008. 113

Figure 3.10: 8-day average chlorophyll-a concentrations as seen from space by

MODIS for Decembers of interest: 2003, 2005 and 2008. The mouth of the Eel River

is starred.

114

viii

Figure 3.11: 8-day averaged model results for December 2003. A: Chlorophyll at 4m

depth produced by the fully coupled modeling framework. B-E: Vertical transect of

the model at 40.64 N, out to 10 km offshore, with the no-river control subtracted from

the full model, for chlorophyll (B), salinity (C), temperature (D) and meridional

velocity (E).

116





velocity (E).

119





velocity (E).

121

Figure 3.14: 8-day average starting at 12/31/2005, the highest Eel River discharge day

in the 2002-2003 water year. A: ROMS phytoplankton. B: MODIS phytoplankton. C:

ROMS results minus the no-river control model results for phytoplankton. D, E, F:

ROMS phytoplankton, detritus, and nitrate respectively, at a 40.64 vertical transect (5

km north of the Eel River mouth) out to 124.45 W. G, H, I: As D, E, F, with the no-

river control subtracted from the results. J, K: ROMS salinity and temperature along

the same vertical transect. L, M: As J and K, with the no-river control subtracted from

the results.

127

Figure 3.15: As Figure 3.14, for the 8-day average starting at 12/27/2006, the highest

Eel River discharge day in the 2006-2007 water year.

129



131



133

Figure 3.18: 8-day averaged phytoplankton results from the no-nutrient river control

subtracted from the with-nutrient river, beginning 02/02/2006, which is also the time

of delivery of the second-largest river discharge event of the water year. Note that

ambient phytoplankton concentration at the mouth of the Eel River is 1.5 mg chl-a/m3,

such that this difference accounts for no more than 4% of the total.

135


subtracted from the with-nutrient river, beginning 02/09/2006. Note that ambient

phytoplankton concentration at the mouth of the Eel River is 0.5 mg chl-a/m3, such

that this difference accounts, as in Figure 3.18, for no more than 4% of the total.

136


subtracted from the with-nutrient river, beginning 02/17/2006. Note that ambient

phytoplankton concentration at the mouth of the Eel River is 0.5 mg chl-a/m3, such

that this difference accounts, as in Figures 3.18-.3.19, for no more than 4% of the total.

137

Figure 3.21: A large phytoplankton bloom generated by the coupled modeling

framework during low-flow conditions in July, with the Eel River given 400x its

normal load of dissolved inorganic nitrogen.

139

ix

Figure 3.22: 11/25/05 example of the model artifact vortex created by momentum over

the Mendocino Triple Junction, and further interactions with the unstable southern

boundary.

141

x

List of Tables

Table 1.1: Granger causality test results. 16

Table 1.2: The squared covariance fractions of the first 8 modes of covariation for the

NPP and Wind Indices with and without the mean of each annual time point removed.

Without removing the mean, there are seven significant modes of variation; removing

the mean creates a system with only six.

20

Table 1.3: 2000-present Eel River papers by topic. Literature reviews and other

particularly useful papers are highlighted. Internal watershed dynamic literature is

excluded.

26

Table 2.1: Parameters used in HydroTrend calculations. 61

Table 2.2: Definitions of terms used in section 2.5. 64

Table 2.3: Lateral boundary conditions used for the ocean circulation model. 71

Table 2.4: Atmospheric forcing fields and their units, as applied directly to the sea

surface with the ERA-Interim dataset.

74

Table 2.5: Powell et al. (2006) parameters used for Powell-NPZD. 78

Table 2.6: Summary of differences between 10 and 1 km model applications. 83

Table 2.7: Summary of model experiments. 84

Table 2.8: HydroTrend results summary for discharge and sediment. Visualized in

Figure 2.23.

84

Table 3.1: Average over-ocean chlorophyll-a satellite coverage in the 39.5-41.5 N, 123-

125 W region of interest near Cape Mendocino for the November-June 2002-2010

climatologies.

98


125 W region of interest near Cape Mendocino for the 8-day averages within December

2003, 2005 and 2008.

99


125 W region of interest near Cape Mendocino for the 8-day averages surrounding each

of the largest Eel River discharge events in the 2002-2009 water years. (The event falls

in the second of three 8-day averages in all years.)

99

Table 3.4: Pattern cross-correlation values (R) and normalized standard deviations for

the November-June model climatologies (2002-2010) as compared to MODIS

climatologies over the same period.

103

Table 3.5: December mixed layer depths and maximum phytoplankton concentrations at

40.64 N, -124.36 W, ocean depth 290m.

107

Table 3.6: Pattern cross-correlation (R) values and normalized standard deviation

comparisons between December 2003 model results and MODIS data.

117



120



122

Table 3.9: Summary of conditions near the Eel River mouth during the largest discharge

event of each water year. Maxima and minima have been highlighted.

124

Table 3.10: Categorization of oceanic conditions and relative strength of the largest Eel

River discharge event of each water year.

124

xi

Table 3.11: Pattern cross-correlation (R) values and normalized standard deviations for

the 8-day averages around 2002 and 2005 events, comparing the model results with to

MODIS data.

126


the 8-day averages around 2006 and 2008 (water year; 2008’s event falls in early 2009)

events, comparing the model results with and without the river with MODIS data.

128


the 8-day averages around the 2003 (water year; the event occurs in early 2004) event,

comparing the model results with and without the river with MODIS data.

130


the 8-day averages around the 2004, 2007 and 2009 (water year; all events occur in

winter-spring of the following year) event, comparing the model results with and

without the river with MODIS data.

132

Table 3.15: The absolute magnitudes of November minus No River November

climatological results within 10 km of the mouth of the Eel River.

142

xii

Introduction

When considering the importance of rivers worldwide to coastal primary productivity, the

Amazon, Mississippi, Congo, Ganges and Yangtze all come to the forefront as examples of key

players. They drain millions of square kilometers apiece, discharging thousands of cubic meters

of freshwater per second into the ocean, delivering massive loads of nutrients and sediment. But

in earth system models, these massive conduits are the only sorts of rivers that appear; anything

less becomes a sub-grid-scale parameterization. For example, in the Community Earth System

Model (Gent et al. 2011), land cells transport a mass of what is functionally distilled water across

their grid. Eventually this perfectly fresh water is spread evenly throughout the adjacent ocean, in

an effort to close the water budget. Little attempt is made to capture lesser river-driven effects

on coastal productivity.

Does it matter? That is the key question that motivates this thesis. Do sub-grid-scale rivers have

significant impacts on offshore primary productivity? If so, effort must be made to include them

more rigorously, for predictive capability at scales helpful to city, state, and regional

policymakers. But there are thousands of smaller rivers in immensely variable settings

worldwide. The best place to start is with a smaller river that seems especially likely to have a

significant impact on offshore environment through its delivery of more than simply freshwater

(its only representation in most global climate models) to the ocean. If such a river fails to alter

offshore dynamics significantly, we can potentially discard many similar rivers with smaller

loads. An obvious candidate in North America is the Eel River, California.

The Eel River discharges into the North Pacific at 40̊ 38.5’ N, just north of Cape Mendocino in

Northern California, delivering large loads of sediments, as well as nutrients, organic matter and

organisms. Its annual discharge (~270 𝑚3

𝑠, Lisle 1990) is about 1% that of the Mississippi, but its

sediment yield (which has historically reached as high as 15 million tons/year) is the highest for

its drainage area (~9500 km2) in the entire continental US (Brown and Ritter 1971).

Furthermore, the Eel River is an especially advantageous choice for a test case because its annual

behavior is dramatic and potentially very sensitive to changes in climate. Driven by the

Mediterranean climate of northern California, it is characterized by low flow during the long, hot

dry season. Then, each winter and spring, storm events flush nutrients down the river to the

ocean, in large pulses (Goñi et al. 2013, Leithold et al. 2005).

These storm flows are out of phase with the other major nutrient input to local coastal biology:

late spring and summer upwelling of cold, nutrient-rich ocean water to the photosynthetically

active surface, as the west coast of North America is the setting for one of the world’s largest

coastal upwelling regions (Smith 1992). The timing and magnitude of these storm events (and

thus the timing (and potentially, the magnitude) of Eel River nutrient delivery) have a great deal

of interannual variability and may be altered by climate change (Morehead et al. 2001, Andrews

and Antweiler 2012, Warrick et al. 2013).

Furthermore, evidence suggests that the fluxes from the Eel River may contribute to

phytoplankton blooms offshore. Ocean color can be used as a surrogate measurement for

chlorophyll and therefore primary productivity (Saba et al. 2011). Satellite imagery off of Cape

xiii

Mendocino has demonstrated spatial, seasonal and interannual variability of ocean color, north

and south of the Eel River's discharge (Legaard and Thomas 2006, NOAA 2012a).

In order to evaluate the potential impact of the Eel River on coastal ocean productivity, two

approaches are taken. In Chapter One, a data-driven analysis unifies satellite ocean color data,

buoy wind measurements, gauging station river discharge rates, and estimations of upwelling

strength. These time series are immensely noisy and complex. Evidence of connection between

the river and the ocean are sought, using statistical techniques (Granger 1969) and empirical

orthogonal functions (Barnett and Preisendorfer 1987). Eel River research literature is also

reviewed, in an effort to summarize the many decades of work that have gone into understanding

the watershed system and offshore processes.

Chapters Two describes a modeling approach used to study the Eel River’s impact on the ocean

at three timescales (climatologically, interannually, and daily events) in Chapter Three. If indeed

the Eel River and other systems like it have a significant impact on coastal productivity, a

regional model that can capture the intricacies of that behavior is a necessary tool for prediction.

Water systems are vital for wildlife, for agriculture, for urban management; improving the field’s

capability to predict outcomes from and feedbacks to rivers is thus equally vital. Extensive and

expensive field data studies such as the products of the River Influences on Shelf Ecosystems

project (Hickey et al. 2010) have been used to drive regional models that examine large rivers; it

is important to discover the extent to which a simpler approach, using existing data from sources

such as the USGS, can be used to create a realistic simulation.

This dissertation constructs a coupled modeling framework to explore the connections between

variability in weather (potentially modulated, slowly, by climate trends), river nutrient delivery

to the ocean, and coastal phytoplankton productivity. Furthermore, it links models from multiple

fields; whereas efforts have been made to force ocean circulation models with real river data

(Castellano and Kirby 2011, Hickey et al. 2010, Warner et al. 2005, Li et al. 2005, Pullen and

Allen 2001, Pullen and Allen 2000), this is an effort to connect an ocean model to a watershed

model, unified beneath the same atmospheric representation. This framework has direct

application to global climate modeling efforts; as a mesoscale entry to the earth system modeling

field, it could be nested within larger simulations that explore a wide variety of climate

scenarios. Although this study is limited to hindcasts, creating a modeling framework that could

be used to create forecasts offers a lens through which to consider a related question: how might

climate change alter the behavior of the river, the coastal ocean, and the nutrient sources for

coastal primary productivity?

Furthermore, models allow us to conduct mechanistic experiments (Sasaki et al. 2006, Gruber et

al. 2006, Capet et al. 2004). Comparing the results of a model with a river similar to that of the

global climate models – which is to say, without any nutrients – with that of a river bearing a

realistic set of nutrients, or an unrealistically large set of nutrients, allows consideration of the

questions that go hand-in-hand with simply ‘does the river matter’: If so, how and why does the

river matter? Is the impact on primary productivity driven by physical or biogeochemical

concerns? How does it compare relative to other oceanic processes such as upwelling? How

might it interact with them? How do these relationships vary from season to season, year to

year? It is these questions that Chapter Three focuses on, through an examination of model

xiv

monthly climatologies, interannual variability, and event-driven analyses of the largest river

deliveries of each water year between 2002 and 2010.

Data analysis and modeling efforts attempt to isolate a potentially very small signal in an

extremely noisy system. But small impacts can accumulate over longer timescales (Allison et al.

2007). If the Eel River appears to have a significant effect on offshore primary productivity, its

inclusion – and that of rivers like it – may be necessary to capture this link in earth system of

land, ocean, and atmosphere.

xv

Acknowledgements

All my gratitude goes to everyone who supported me throughout this program, from faculty, to

students, to staff. Thanks to my advisor, Zack, and the rest of my committee, Wayne, Dennis

and Bill. Special thanks also to Inez Fung, Mary Power, Jeff Dorman, Jonah Pilvia-Scott and

Albert Kettner for their assistance, encouragement, and mentorship, and to Dave, Myrrh,

Rebecca, Celia, Daala, Alice, Jill, Lain, Trudy, Gull, Lonny, Anna, Melissa, Jon and Cyrene for

their tireless support. Thanks above all to my family: Mycol, Ryan, Mom and Gary, without

whom this would not have been possible.

1

Chapter 1

1.1 Introduction

1.2 The Eel River: Overview

1.3 The Eel River: Literature Review

1.3.1 1910-1979

1.3.2 1980-1989

1.3.3 1990-1999

1.3.4 2000-present

1.3.5 Empirical Sediment Models and the Eel River

1.4 Data Analysis: Overview

1.5 Estimation of NPP from ocean color data

1.6 MODIS data

1.7 NBDC buoy data

1.8 USGS gauging station data

1.9 Methodology: Granger’s Test for Predictive Causality

1.10 Results: Granger Causality

1.11 Methodology: Canonical Correlation Analysis

1.12 Results: CCA

1.13 Discussion and Conclusion

1.1 Introduction

In order to characterize the possible importance of smaller rivers on coastal ocean primary

productivity, the Eel River is chosen as a test case for its depth of previous research and

extremity of behavior, with most of its discharge occurring over a few days a year as driven by

winter storms. After reviewing historical research on the Eel River, data are selected for analysis

in an attempt to find connections between river and ocean behavior. By combining satellite

ocean color data as an estimate of Net Primary Productivity and time series of river discharge,

wind direction near the mouth of the river, and a monthly Upwelling Index (to identify times

when the system is experiencing upwelling), it is possible to estimate when the river might be

important to offshore primary productivity. It is also possible to estimate which direction its

plume might be going, with sediments and nutrients entrained within for possible biological

uptake.

Although qualitative observation of the time series provides some interesting insight, in order to

more robustly search for the river’s signal amid the noise of everything else going on, Granger

causality (Granger 1969) and Canonical Correlation Analysis (Barnett and Preisendorfer 1987)

techniques are used to examine the time series quantitatively. Finally, results and implications

are discussed in detail, in terms of what can be gleaned from these analyses in order to direct

further research.

2

1.2 The Eel River: Overview

The Eel River is the third largest watershed entirely contained in the state of California. It is

315 km long, flowing across 9540 km2 of basin, and has the South, Middle, and North Fork Eel

Rivers, plus the Van Duzen River, as tributaries (see Figure 1.1). It begins on Bald Mountain in

the Pacific Coast Range, 1903 meters above sea level. It is used for groundwater recharge,

recreation, industry, agriculture and for municipal water supply (Brown and Ritter 1971). This

water use does not seem to heavily influence the nutrient content of the river (Madej et al. 2012,

Goñi et al. 2013).

The Eel River’s discharge is storm-driven, with virtually no precipitation from July-September

producing, in turn, low flow during that time. The winter storm flow season begins, at the

earliest, in late November, with the majority of the discharge occurring between December and

March; on average, 90 percent of all precipitation falls between October and April (Lisle 1990).

These flows can be astonishing in scope, up to 26,500 𝑚3

𝑠 on 12/23/1964, which comprises the

largest recorded peak discharge of any river in California (Lisle 1990).

This event-driven flow, combined with the Coast Ranges’ erosive bedrock, rapid uplift, and

human disturbances (logging practices, primarily), also produces a stunning riverine sediment

load, historically averaging ~2.6 x 10^7

metric tons of suspended sediment a year (Brown and

Ritter 1971; Syvitski et al. 1999; Wheatcroft and Borgeld 2000), although in recent decades there

is strong evidence that the sediment load is in decline (EPA 1999, 2002, 2003, Warrick et al.

2013, Warrick 2014). Because the river has a very small flood plain and virtually no estuary, the

majority of the suspended sediment load is transported directly into the Pacific Ocean

(Wheatcroft et al. 1997). Initial plume deposition of the sediment can range up to 100 km from

the river mouth, but secondary resuspension of sediment by gravity waves during storms causes

perhaps the majority of the transport, both along and across-shelf (Puig et al. 2004). Warrick

2014 suggests that previous studies have overestimated secondary transport of sediment across

the shelf and into deeper waters.

3

Figure 1.1: The Eel River watershed (Lisle 1990)

1.3 The Eel River: Literature Review

1.3.1 1910 - 1979

Though there were a few earlier management recommendation reports, as well as United States

Geological Survey (USGS) discharge data collected as early as 1910, research on the Eel River

began in earnest in the early 1950s, including USGS water quality sampling that began in 1951.

Surveys of fish populations by the California Fish and Game department, and academic

geomorphological studies (Maxon 1952), were the primary interests at the time. There were a

few major Eel River floods over these decades, most notably in 1955 and the infamous

Christmas flood of 1964, the worst flood in recorded history. In 1959, perhaps spurred on by the

former event, the USGS began collecting suspended sediment concentration and total discharge,

and continued to do so until late 1980. (USGS 2012)

A 1971 USGS Water Supply Paper by Brown and Ritter (Brown and Ritter 1971) is the first

expansive published report about Eel River sediment transport, and Ritter another USGS report

considering Eel River sediment (Ritter 1972). However, non-government-report literature

pertaining to offshore Eel River sediments only begins to appear in the mid-1970s (Piper 1976),

with the first academic study of the whole region, rather than a specific physical feature, coming

out of UC Santa Cruz in 1980 (Griggs and Hein 1980). Griggs and Hein present an estimate of

total sediment delivery utilizing USGS gauging data, sediment mineral composition data, as well

as a spatial analysis of suspended sediment being transported via river plumes using the 1970s

satellite LANDSAT. Other inferences of currents on the Eel River shelf via satellite data

occurred throughout the 1970s, (Carlson and Harden 1975, Pirie and Steller 1977), as well as

drift card studies (Carlson and Harden 1975) and studies of historical wind records (Nelson

1977).

4

1.3.2 1980 – 1989

Offshore sediment studies continued through the 1980s, including research on thermogenic

hydrocarbons (Kvenvolden 1981), oxygen isotopic composition of fossils (Dodd 1984), and

paleogene rocks (Underwood 1985). In 1985, on the basis of physiographical and

sedimentological criteria, Borgeld et al. (1986) defined the Eel River shelf to extend across 55

km from Cape Mendocino to Trinidad Head. In 1986, a study entered the literature providing

data on Eel River gravity wave heights and periods (Corson et al. 1986). Finally, at the end of

the decade, a University of Washington study (Leithold 1989) demonstrated that fine-grained

shelf deposits of sediment do preserve a distinguishable, if subtle, record of depositional

processes and individual events.

Importantly, in 1982, NOAA launched a buoy about 20 km offshore of the Eel River mouth at

40.724̊ N, 124.578̊ W, called Station 46022 (LLNR 500). Time series of wind direction, speed,

peak gust speed, significant wave height, dominant wave period, average wave period, mean

wave direction, sea level pressure, air temperature, sea surface temperature, dewpoint

temperature, station visibility, pressure tendency and tidal levels are available from this period

onwards. The buoy received a sensor upgrade in 1996, adding continuous (rather than averaged)

winds data and spectral wave density data. (NOAA 2012a)

1.3.3 1990-1999

Biology’s interest in the Eel River exploded with the publication of local freshwater ecology

experiments in 1989-1990 (Feminella 1989, Power 1990a), culminating in a landmark Science

paper (Power 1990b), and several major Ecology papers in 1992 (Power 1992a, 1992b, 1992c;

Power’s extensive Eel River-related bibliography can be found at Power 2014). Power and her

collaborators have produced many dozens of papers and several books on Eel River biology,

from ecological experiments to genetic structure analysis and everything in between, between

then and now, with an increasing focus on nitrogen limitation in the Eel River, and its

relationship to storm event-driven river scouring effects (Marks et al. 2000), as well as the

growth of Cladophora and other nitrogen-fixing algae found to grow along the river annually

(Schade 2010). The possibility that storm-scouring leads to infrequent delivery of nitrogen-

fixing Cladophora to the Eel River mouth as a source of nitrogen for coastal ocean productivity

is a line of thought that came out of this research. River-watershed exchange (Sabo and Power

2002; Bastow et al. 2002) was also a major topic of study. Nor were they the only ones; made

aware of this interesting system, biological study within the Eel River basin has intensified ever

since. However, as this thesis does little with internal watershed dynamics from the biological

standpoint, Eel River watershed biological systems research will not be further reviewed here.

Eel River sediment studies continued as well. There were a few cruises looking at specific

locations of geomorphological interest, but the major results from the 1990s came from the

continued work of Borgeld, notably joined by Wheatcroft, Sommerfield and Nittrouer in 1996-

1997 (Wheatcroft 1996; Wheatcroft 1997), who were very interested in the rapid and widespread

dispersal of flood sediment on the northern California margin.

5

Led by Nittrouer and joined by many others, the STRATA FORmation on Margins

(STRATAFORM) Program, supported by the Office of Naval Research, was created in the late

1990s (Nittrouer 1999) to study and model the relationships between marine and terrestrial

events, physical processes, and stratigraphy; it had two major research sites, and one was Cape

Mendocino and the Eel River (while the other was in New Jersey). STRATAFORM produced

an enormous number of publications and laid the foundations for a research program that

continues to collect data to this day under various auspices.

In 1999, Volume 154 of Marine Geology published 27 STRATAFORM-related papers, most of

these focusing on the Eel River, and data collected between 1995-1997, most notably during the

major 1995 flood event. Important results included measurements of the size and settling

velocity of sediment particles (Sternberg et al. 1999), sediment flux measurements taken with

moored sediment traps (Walsh and Nittrouer 1999), results from monitoring tripods measuring

hourly currents, bottom pressure, suspended-sediment concentration, and seabed roughness

(Ogston and Sternberg 1999; Cacchione et al. 1999), camera and sonar studies of sediment bed

features (Wright et al. 1999; Goff et al. 1999), replicate box cores were collected across many

cruises to study biogeochemical signatures in particulate organic carbon and physical spatial

variability (Drake 1999; Leithold and Hope 1999; Alexander and Simoneau 1999), acoustic

swath bathymetric mapping and GIS analysis (Borgeld et al. 1999; Lee et al. 1999), a towed

electromagnetic survey to study shelf porosities (Evans et al. 1999), 7Be,

210Pb and

137Cs

geochronolgical studies of Eel River muds (Sommerfield and Nittrouer 1999; Sommerfield et al.

1999), and analyses of offshore subsurface gas (Yun et al. 1999) and Dissolved Organic

Phosphorus (Monaghan and Ruttenberg 1999). None of this data is used directly in this thesis,

but laid the foundation for further analysis throughout the following decade that we consider

below in section 1.3.4.

There were also modeling efforts in early STRATAFORM. An analytical model to represent

two-dimensional, laminar, non-hydroplaning mudflow resulting from deep water submarine

slides (Huang and Garcia 1999) was validated against laboratory flows rather than

STRATAFORM data, while a sediment-transport model involving bed-armoring was designed to

understand important parameters in that process (Reed et al. 1999). Another analytical model,

this one utilizing 2-D solutions to the state of stress on an infinite slope, was utilized to

understand slope-failure mechanics (Mello and Pratson 1999). A two-dimensional, across-shelf

sediment-transport model was forced with Eel River shelf storm waves to understand storm

deposition (Zhang et al. 1999).

Finally, among the STRATAFORM modeling publications in 1999 were a pair of papers were

by James Syvitski's group, about estimating Eel River sediment discharge to the ocean (and to

some degree the fate and transport of that sediment offshore by the river plume): (Syvitski and

Morehead 1999; Morehead and Syvitski 1999); a literature review of this modeling effort and its

heritage can be found in section 1.3.5.

6

1.3.4 2000-present

From 2000 onwards, there is simply too much research to go through; a table of relevant Eel

River papers sorted by topic is listed at the end of the chapter, in Table 1.3. Each topic, however,

can be briefly discussed in terms of major findings, lines of research, and interesting arguments.

Biogeochemical cycling - anaerobic conditions: Early in the decade, there were a variety

of papers looking at methane seeping from sediments, ultimately reviewed in (Levin et al.

2010). Most interesting were distinct microhabitats of microbial mats, which oxygen was

unable to penetrate, thus creating anaerobic conditions at sediment depths that would

normally have significant oxygen content. Starting in 2009, both iron and manganese

oxidation-reduction biogeochemistry have been explored in depth; it appears that benthic

manganese fluxes from the Eel River continental shelf are an order of magnitude higher

than other regional shelf settings (McManus et al. 2012), and multiple groups have found

evidence of co-variation of redox rate with organic carbon content. It has been proposed

that reactive organic carbon from riverine discharge may remobilize otherwise

unavailable iron (Severmann et al. 2010); for the latest review and results, see (Roy et al.

2013).

Biogeochemical cycling – biological perturbation of shelf-held sediments: A few studies

were performed looking for biological alteration of how flood deposits are physically

structured; there is evidence that bioturbation intensity has been constant for thousands of

years (Sommerfield et al. 2001).

Biogeochemical cycling – characterization of Eel River-delivered organic matter: A

particularly crucial topic, the major result of the past decade of research on this topic is

that organic matter in sediments appears to break down much more slowly than had been

expected (Blair et al. 2003, Drenzek et al. 2009). There is a wide variety of

measurements available, including Carbon to Nitrogen ratios and isotopic

characterization of various particle types. Most recently, particulate organic matter was

thoroughly characterized during both low and high flow regimes (Goñi et al. 2013).

Sediment fate and transport – physical characterization: Studies on this topic look

particularly at physical concerns, such as flocculation, accumulation, and settling

velocity. There is strong evidence that large portions of flood sediment are delivered to

the Eel River Canyon (Mullenbach and Nittrouer 2006); evidence is contradictory,

however, about whether or not periods of extreme sediment concentration induce massive

floc sizes (and settling rates).

Sediment fate and transport – gravity flows: By far the most research has gone into the

discovery (summarized in Wright et al. 2001) and subsequent characterization of a

secondary mechanism for sediment transport other than plume delivery from the inner

shelf to the midshelf. It was a major surprise when storm resuspension of older

sediments into gravity-driven fluid muds were found to occur far more often than had

been thought possible (Puig et al. 2003). It is now believed that this secondary process

dominates sediment fate on the continental shelf (Guerra et al. 2006). Numerous efforts

have been made to conceptually and empirically model this effect, culminating in a three-

dimensional hydrodynamic model of sediment transport mechanisms (Harris et al. 2005).

An excellent literature review is provided in (Wright and Friedrichs 2007). Most

recently, the idea that this secondary mechanism is unnecessary to explain sediment

7

transport due to an overestimation of total sediment delivered to the shelf has presented a

major challenge to these findings (Warrick et al. 2013, Warrick 2014).

Sediment fate and transport – sequence stratigraphy and climate change: There have been

attempts to characterize and interpret stratigraphic preservation of flood events as a

climate change signal. Whether it is climate change (Sommerfield et al. 2002) or land

use (Leithold et al. 2005) driving the recent stark increase in marine sedimentation is a

subject of debate. What is clear is that intense biological mixing intensity on the Eel

River shelf dissipates most signals captured in heterogeneity between 3-15 years

(Wheatcroft and Drake 2003), except for episodic sedimentation from Eel River flood

events, which can preserve event beds and transient signals for at least a thousand years

(Sommerfield and Wheatcroft 2007). A book, From Sediment Transport to Sequence

Stratigraphy, provides an overarching look at the topic (Nittrouer et al. 2007).

Modeling efforts – 3D ocean circulation: This ‘topic’ comprises only two papers, but

their direct significance to our subsequent modeling effort makes them worthy of

discussion. A purely physical three dimensional model at 1 km resolution, run as a 40-

day simulated the major 1997 Eel River flood (Pullen and Allen 2000). They used the

Princeton Ocean Model (POM) in its Naval Research Laboratory's Pacific West Coast

Model (NRL PWC; Clancy et al. 1996) configuration for this purpose, and were able to

reasonably reproduce the onshore velocity fields measured by STRATAFORM tripods.

They found that coastline irregularities were important to generating local eddies, and

that the mixing of the freshwater plume influences the velocity structure of the shelf flow.

A later followup study (Pullen and Allen 2001) performed 3 km and 9 km resolution

model runs, documented strong alongshore variability in wintertime flow, and reproduced

it with good agreement. They also noticed a robust anticyclonic eddy that forms when

strong poleward winds weaken and reverse direction during winter storms.

1.3.5 Empirical Sediment Models and the Eel River

Empirical sediment models are designed to provide data rich estimations of a watershed’s river

discharge and sediment transport. Given atmospheric forcing (typically based on temperature

and precipitation), and parameterized based on specific attributes of the watershed being

modeled, they can often generate useful predictive results. Their weakness is a lack of

portability (as what is good for the Mississippi may not be good for the Hudson) and a tendency

to obscure basic mechanics with their major simplifications. They are unsuitable for trying to

tease out new knowledge and understanding of the mechanistic nature of watersheds – but very

useful as a first-order approximation of watershed behavior.

In 1995, an empirical model called RIVER3 was developed to simulate the discharge and

sediment load of rivers (Syvitski and Alcott 1995). The hydrology portion of this model was

exceedingly simple, however, running at constant temperature with pre-defined "seasons" for

precipitation distribution into snow, ice and rain. In 1998, the first version of the lumped

empirical model HydroTrend was published (Syvitski et al. 1998a), adding a great deal of

missing detail, not just about atmospheric input but also canopy interception, improved

subsurface flow, and flood algorithms. HydroTrend shared the same sediment load models as

RIVER3, without adjustment: suspended load and bedload calculated separately, using empirical

sediment rating curves.

8

These curves have been used and improved by engineers for most of the 20th century (reviewed

in Syvitski et al. 2000). In 1992, Syvitski analyzed data from 280 rivers and found sediment

loads to be a log-linear function of basin area and maximum elevation (Milliman and Syvitski

1992). As part of an effort to generalize sediment rating curves to ungauged basins, and

understand their sensitivity to various environmetnal variables, 57 rivers, including the Eel

River, were studied (Syvitski et al. 2000); later the Eel River was included an effort was led to

characterize global variability of sediment flux from concentration and discharge (Meybeck et al.

2003; Syvitski et al. 2003). Separately but relevantly, a worldwide analysis of small

mountainous river systems and their delivery of particulate organic carbon created a set of POC

rating curves (Wheatcroft et al. 2010).

Sediment rating curves are often too simple, as only rivers that drain high sediment-yield, single-

source areas demonstrate a simple first-order relationship of suspended load versus discharge

(Syvitski et al. 1998a). RIVER3 (and HydroTrend) addressed the seasonal hysteresis of

sediment concentration vs. river discharge by separately calculating suspended sediment

production for each individual source of water (overland flow, groundwater flow, snowmelt).

Bedload transport was then determined through an estimate involving sand grain and fluid

density, gravity, the slope of the river bed, bedload efficiency and the limiting angle of repose of

sediment grains lying on the river bed (Bagnold 1966).

HydroTrend was applied to the Eel River on both daily and interannual timescales, and did a

reasonable job of reproducing Eel River discharge. Its sediment production lacked some of the

variability of the actual data, since, for example, it cannot capture the first flood of the water year

containing a higher sediment concentration than subsequent floods.

Simultaneously, Syvitski published PLUME1.1 (Syvitski et al. 1998b), a two-dimensional

advection-diffusion equation modeling a turbid hypopycnal plume emanating from the river

mouth. PLUME1.1 was a significant advance over GRAIN2 (Syvitski and Alcott 1993), which

traced individual streamlines out from the river mouth, solving a simple reaction equation for

each one. It could use HydroTrend output as forcing, but, of course, only captured initial

advection and deposition of sediment, rather than the important secondary transport along the Eel

River shelf. Once again this model was applied to the Eel River, but with limited success in

accurately depicting accumulation rate on the shelf.

The following year, PLUME was forced by STRATAFORM data to reproduce the plume during

the 1995 flood event from January 7-15 (Morehead and Syvitski 1999). It estimated the plume

traveling over 60 km north of the Eel River mouth, with most sediment deposited within 30 km.

Furthermore, they attempted a climactic paleo simulation at 18,000 years before the present, but

this is less compelling, as PLUME's lack of ability to capture secondary processes makes it not

useful for long time scales. They also simulated the Eel River using collected climatic statistics

for the last fifty years (Syvitski and Morehead 1999), with general success regenerating USGS

statistics for Eel River discharge and sediment loads.

The next model developed in the chain was SEDFLUX (Syvitski and Hutton 2001), which

integrated a suite of process-based models to predict the lithologic character of basin

9

stratigraphy. They attempted to reproduce the Eel River Margin (Morehead et al. 2001), but

again did very little with gravity flows. SEDFLUX had the capacity to capture hyperpycnal

flows and debris flows, but it only attempted to add cross-shore transport due to ocean wave

sediment resuspension in Sedflux2.0 (Hutton and Syvitski 2008). Application of Sedflux2.0 to

the Eel River for long-term sediment accumulation has not been published; it used the Po River

as its test case.

HydroTrend also received an update in 2008, becoming HydroTrend 3.0 (Kettner and Syvitski

2008). HydroTrend 3.0 enjoys new suspended sediment algorithms, an improved routine to

simulate sediment delivery fluctuations from ice storage and release, a sediment trapping routine

to account for lakes or reservoirs, multiple delta outlets, and a sequential rather than statistical

use of climate observations, for direct comparison and validation. It uses much of the sediment

rating curve analysis from Syvitski et al. (2003), and additionally includes basin lithology and

human activity as parameters (Syvitski and Millman 2007).

The other notable modeling effort for empirical sediment processes in the Eel River is much

more modern; an artificial neural network (ANN) model was developed and trained by linking

six single-station models (Nourani and Kalantari 2010). It enjoyed reasonable results, and led to

a second ANN model based not on linked single stations but geomorphology (Nourani et al.

2014), which produced better performance by emplying spatially variable factors of the

subbasins, rather than being a fully lumped model. Simultaneously but independently, the ability

of least square support vector machine (LSSVM) modeling to capture Eel River behavior was

explored (Kisi 2012), and it slightly outperformed the first ANN model. Both methods were

superior to sediment rating curve modeling for upstream stations, but downstream, the sediment

rating curves were still superior. However, when both stations were integrated to provide a total

flux, LSSVM and ANN both outperformed the sediment rating curve model.

1.4 Data Analysis: Overview

With this surfeit of available data, an analysis is in order, to estimate the first-order effects of the

sediment and nutrient-laden Eel River storm plumes on coastal Net Primary Productivity. There

are four easily accessible, immediately relevant time series:

1) The Oregon State University Net Primary Productivity dataset (Behrenfeld 2005)

2) The NOAA NBDC buoy closest to the mouth of the Eel River, which provides wind direction

(NOAA 2014)

3) The USGS gauging station best suited to continuous time series of discharge, which tells us

when significant Eel River plumes are occurring (USGS 2012)

4) The NOAA Coastal Upwelling Index, which tells us when significant coastal upwelling (and

delivery of nutrients) is occurring (NOAA 2013a)

The combination of these time series are plotted in figures 1.2 and 1.3. The multi-year figure has

clearly visible seasonal patterns, with the upwelling winds appearing as a negative (northerly)

index value in summer simultaneous with a positive (north of the cape) NPP distribution, and

then more southerly winds in winter coinciding with complex NPP behavior. The grid of single-

10

year figures have the upwelling and significant Eel River discharge months indicated to highlight

the different behaviors visible in each season.

A simple statistical test that detects for the potential for causality rather than only correlation,

called the Granger Test, can give us a sense of if or when the wind direction time series is a

predictor of the location and magnitude of nearby coastal primary productivity – phytoplankton

blooms affected by the Eel River plume (or lack thereof). A much more complex and nuanced

analysis can be performed using the Canonical Correlation Analysis, the top tier of the hierarchy

of correlative analysis tools. CCA looks for modes of variation within a given dataset, and co-

variation between datasets, such as the NPP and wind direction time series. The relative

amplitudes of these modes can give us insight into when a co-variation was important, and when

it was not.

Figure 1.2: the NPP (blue, left Y axis) and Wind (red, right Y axis) Indices, 2003-2012. A

positive value of the NPP index indicates more NPP to the north of Cape Mendocino than the

south, while a negative value indicates the opposite. If it is zero, equal production is occurring in

both regions. A positive value of the Winds index indicates that on average for that 8-day point,

the wind spent more time blowing towards the north than the south; a negative value again

indicates the opposite; and if zero, an equal amount of time was spent blowing in either direction.

Note that during each summer, a strongly negative Winds index is observing upwelling

conditions, a strong seasonal signal.

11

Figure 1.3: Yearly NPP and Wind Index plots, with upwelling and significant months of river

flow shaded. See Figure 1.2 for interpretation of the NPP and Wind indices.

1.5 Estimation of Net Primary Productivity from Satellite Ocean Color Data

Ocean color can be used as a surrogate measurement for chlorophyll and therefore primary

productivity (Saba et al. 2011). The Vertically Generalized Production Model (VGPM;

Behrenfeld and Falkowski 1997a) is a commonly used “chlorophyll-based” algorithm for

estimating Net Primary Production. It is similar in form to the early models of Ryther and

Yentch (1957) and Talling (1957).

The VGPM assumes that NPP can be expressed as a function of chlorophyll concentration, but as

NPP is a rate and chlorophyll is a standing stock, a chlorophyll-specific assimilation efficiency

for carbon fixation must be estimated. This is a description of how photosynthetic efficiency

under light-saturated conditions varies physiologically in the environment, called Pbopt, based on

daily integrated production measurements. Pbopt is the maximum daily net primary production

found within a water column, in units of mg carbon fixed per mg chlorophyll per hour. In the

standard VGPM, Pbopt is temperature dependent (Behrenfeld and Falkowski 1997b), and total

water column NPP is a function of chlorophyll, Pbopt, day length and a volume function that

12

combines euphotic depth (calculated using the Morel and Berthon 1989 Case I model) and a

data-driven parameterization of light penetration into the water column (Platt and

Sathyendranath 1993). Therefore, the data that goes into the ocean color analysis is chlorophyll,

photosynthetically active radiation, sea surface temperature, and day length, all of which we get

from MODIS.

1.6 MODIS data

MODIS (or Moderate Resolution Imaging Spectroradiometer) is an instrument aboard the Terra

and Aqua satellites. Combining both satellites’ reach, MODIS views the entire Earth’s surface

every 1-2 days, acquiring data in 36 spectral bands. This data analysis uses the new

MODIS.R2013 reprocessing results for chlorophyll, cloud-corrected incident daily

photosynthetically active radiation, sea surface temperature and day length, regridded to 1/12 of

a degree in both latitude and longitude, and to 8-day averages in time (NASA 2013). NPP “north

of the mouth of the Eel River” is considered to be from 40.5̊ to 41.08̊ N, roughly 50 km.

Southern NPP is from 39.92̊ to 40.5̊ N. The analysis goes 0.83̊ W off the coast, following the

shoreline to normalize the distance offshore.

13

Figure 1.4: Simplified visualization of where satellite data are selected for analysis.

An index of geographic distribution is then constructed by simple normalization: the difference

between northern and southern NPP, divided by their overall sum. When the NPP Index is 1, all

growth is north of the cape; when it’s 0, there is an equal amount of growth north and south of

the cape; and when it’s -1, all growth is occurring to the south.

1.7 NBDC Buoy Data

The National Data Buoy Center Station 46022 (LLNR 500) is a 3-meter discus buoy 17 nautical

miles WSW of Eureka, California, at 40.724̊ N, 124.578̊ W. It maintains an ARES 4.4

instrumentation payload, measuring sea level height, air temperature at 4m above the sea surface,

wind speed and direction at 5 meters above the sea surface, humidity at the sea surface, and sea

surface temperature at 0.6 meters below the sea surface. Of these, we’re mostly interested in

wind direction, because it gives us an indicator of the direction that the Eel River freshwater

14

storm plume is being advected on the surface of the ocean. Once again we construct a

directional index, this time of the frequency of southerly minus the frequency of northerly winds

within a given period, divided by the sum of both frequencies. As the NPP data are in 8-day

averages, that is the period chosen for the Wind Index as well.

The wind direction sensor ranges from 0-360 degrees, taking data at 1.71 Hz. It has averaging

periods every 2 and 8 minutes, a resolution of 1.0 degree and accuracy of ±10 degrees. A unit-

vector average is used to calculate the average wind direction, in which unity serves as the length

of the vector, and the wind direction observations serve as the orientation of the vector. The u

and v components are then calculated for each observation. Then the average u and v

components are computed, and the average wind direction is derived from arctan(𝑢

𝑣) (NOAA

2014).

1.8 USGS gauging station data

USGS gauging station 11477000, Eel River at Scotia, CA (40.492̊ N, 124.099̊ W) has been

collecting discharge and gauge height data since October 1910, and continues to this day. It

collected suspended sediment concentration and total suspended sediment load from 1959-1980.

From 1951-1998 water quality data was regularly collected, including temperature, total

nitrogen, organic nitrogen, ammonia, nitrite and nitrate concentrations. This stream site drains

over 80% of the Eel River Basin (it is, notably, missing the Van Duzen tributary). Nearest the

mouth of the river, the Eel River at Fernbridge gauging station 11479560 only collects gauge

height and a webcam image. Primarily our interest is in the discharge data, which is collected

using a USGS Type AA Current Meter, which accurately measures streamflow velocities from

0.025-7.6 meters per second, which are then multiplied by a river subsection area to get that

portion of the discharge. Whether or not Eel River flooding goes beyond the current-meter

method’s ability to estimate discharge is unknown, but the literature has taken these

measurements as reasonable estimates for as long as literature has existed.

1.9 Methodology: Granger’s Test for Predictive Causality

A time series X is said to Granger-cause Y if it can be shown through a series of tests on lagged

values of X and Y that those X values provide statistically significant information about future

values of Y (Granger 1969). Using the R package lmtest (Hothorn 2014), a Wald test is used to

calculate a maximum likelihood estimate, compared against a chi-squared distribution. Failure

to reject the null hypothesis is equivalent to rejecting the hypothesis that X does not Granger-

cause Y (Toda and Yamamoto 1995). Granger causality is a useful tool, but one that must be

used with care – clear conclusions are hard to find outside of a simple 2-dimensional system.

Still, insights can be gained by examining where, when, and how strongly, Granger causality

appears.

Applying Granger causality theory to two time series (the NPP and Wind indices) requires taking

the first differences of each time series in order to render them stationary; otherwise the

regression tests will be meaningless (Lutkepohl 2006). Furthermore, the time series were first

detrended and deseasonalized with moving averages, in order to capture interannual variation

rather than just the major seasonal signal. Finally, due to the extreme difference in dynamics

15

between summer and winter, Granger causality was tested for not the entire time series, but

separately for the upwelling-dominated months of the time series, and for months of the time

series in which extreme (greater than 1% annual discharge during a given day of year) Eel River

discharge took place. A lag of 3 timepoints was used – that is to say, what is being tested is

whether a model that uses both Wind and NPP to predict NPP, as well as just NPP by itself,

using up to three values behind a given timepoint for that prediction.

1.10 Results: Granger Causality

Table 1.1 shows the probability that the null hypothesis, that is to say, that the Wind Index does

not predict the NPP Index, and vice versa, is true. A small value indicates that the null

hypothesis should be rejected, thus implying that the Wind Index is a potentially useful predictor

of the NPP Index (or vice versa). Granger causality is tested in both directions, and is often

useful for determining which variable is controlling which (commonly explained to be an

attempt to solve the “chicken and the egg conundrum”). That is not a serious question in this

case, however: since phytoplankton have no known feedback on atmospheric momentum

dynamics, a result that NPP-predicts-the-Wind would be absurd to interpret at face value.

However, given the fact that some wind events happen near the end of one 8-day average, thus

potentially driving the next 8-day average NPP, or are split between two averages, that could

explain the possibility of the lag apparently reversing, such that the NPP seems to be predicting

the wind.

To the extent that a signal of the wind driving river plumes to induce phytoplankton blooms

could be captured this way, it is reasonable that the signal would not appear equally strongly

from year to year, because of a third factor: how much Eel River discharge is available to affect

the system. To give us a sense of the relative presence of the river from year to year (mostly

flowing, by definition, during the storm season), Table 1.1 includes the summed discharge from

a given (September-August) water year.

16

Table 1.1: Granger Causality results.

Water

Year

(2003 is

September

2003-

August

2004)

Pr(>F):

Wind

predicting

NPP,

upwelling

season

NPP

predicting

Wind,

upwelling

season

Wind

predicting

NPP,

storm

discharge

season

NPP

predicting

Wind,

storm

discharge

season

Total Water

Year Discharge

2003 0.9988 0.7635 0.1103 0.7193 6.88E+009

2004 0.2215 0.2399 0.1362 0.6819 6.25E+009

2005 0.9782 0.3525 0.07097 0.08366 1.30E+010

2006 0.1095 0.04784 0.088 0.5001 3.77E+009

2007 0.5439 0.3473 0.3844 0.5667 4.51E+009

2008 0.3589 0.7414 0.6005 0.938 3.37E+009

2009 0.3396 0.9553 0.8082 0.8001 6.29E+009

2010 0.9127 0.0225 0.1439 0.1048 8.50E+009

2011 0.868 0.8137 0.2375 0.1824 4.28E+009

Table 1.1 is represented visually in Figures 1.5 (for the upwelling-dominated system) and 1.6

(for the potentially storm discharge dominated system). The first thing we see is that we cannot

reject the null hypothesis, ever, at a 95% confidence level, with a single exception in the 2006

upwelling season. Given the complexity of the system, and the potentially very small effect of

the signal of the Eel River on the coastal ocean, this is not surprising. However, patterns still

emerge. During the upwelling season, other than in 2006 (and NPP-predicting-wind in 2010),

there is never a significant possibility of wind direction predicting NPP geographic distribution

in the positive direction, which is a reasonable result, since we know from the data that when

upwelling winds (blowing towards the south) are strongest, NPP is larger in magnitude towards

the north of the cape.

During the storm season, winds predict NPP far more significantly than the other way around in

six out of nine years analyzed: 2003, 2004, 2005, 2006, 2007, and 2008. Winds predict NPP

most successfully, at an 85% confidence level or better, during the years of most significant Eel

River discharge: 2003, 2004, 2005, and 2010, which are all the years of relatively extreme Eel

River discharge. 2009, which had more storm flow than 2004, is an outlier, lacking correlation.

That NPP-predicting-Wind has drastic improvements in correlation in 2005 and 2010, the two

main years of exceedingly high Eel River discharge, is also interesting, since we would expect,

due to the weird lag effects discussed at the top of this section, for, when the time series

prediction appears to reverse due to effects related to the river, the river to be important.

Naturally, this could also all be coincidence. Further analysis of additional years added to the

record over time will provide further insights, but in the end Granger causality’s lack of strong

results is just another way of saying that this system is complicated.

17

Figure 1.5: Granger causality test results, Wind and NPP Indices during the upwelling-dominated

period.

18

Figure 1.6: Granger causality test results, Wind and NPP Indices during the storm-dominated

period.

1.11 Methodology: Canonical Correlation Analysis

Canonical Correlation Analysis (CCA) is at the top of the hierarchy of regression modeling

approaches, described in detail in Barnett and Preisendorfer (1987) and then in a text,

Priesendorfer (1988), and compared to other statistical methods used in climate research in

Bretherton et al. (1992). CCA computes linear combinations of a set of predictors to maximize

relationships, in a least square error sense, between a given set of time series. By breaking a

field of data down into its empirical orthogonal functions (EOFs) using eigenvalues and

eigenvectors, patterns in time and space emerge. Singular Value Decomposition (SVD) analysis

of two fields makes it possible to examine covariability within them. The method is well-

summarized in Bjornsson and Venegas (1997).

As we only have one spatial point for the wind (the NBDC buoy), we perform an analysis on the

Wind Index and the three-dimensional NPP field (space by space by time) that has been reduced

to two dimensions (space by time) when transformed into the NPP Index. Our row vectors are

now composed of the 8-day average time series for a given year. Our column vectors are the

same days-in-year point within varying years (see Figure 1.6). In this way we can study

interannual variability, rather than spatial variability.

19

Figure 1.7: The matrix F to be decomposed into EOFs, mapped to have each row as one year’s

worth of time series, and each column a time series of observations for a given date within a

year. Figure adapted from Bjornsson and Venegas (1997).

20

1.12 Results: CCA

By performing Canonical Correlation Analysis, we generate two sets of singular value

decompositions: with and without the mean of each time point removed. It is a safe assumption

that with the seasonality present, upwelling will dominate, but it is still interesting to see the

patterns in which upwelling covaries with NPP.

Table 1.2: The squared covariance fractions of the first 8 modes of covariation for the NPP and

Wind Indices with and without the mean of each annual time point removed. Without removing

the mean, there are seven significant modes of variation (the largest of which is clearly

upwelling); removing the mean creates a system with only six.

Mode of

variation

Squared Covariance

Fractions: Unmodified

NPP and Wind Indices

Squared Covariance

Fractions: NPP and Wind

Index Anomalies

1st 0.474239 0.283305

2nd 0.150658 0.214903

3rd 0.114515 0.17581

4th 0.090237 0.140652

5th 0.075368 0.108192

6th 0.053594 0.077138

7th 0.041389 3.51E-17

8th 5.61E-17 3.05E-17

21

Figure 1.8: The first and largest modes of covariation (EOF1) for NPP (A) and Wind (B) in the

case where we analyze the system without removing the interannual mean from each point, and

for NPP (C) and Wind (D) when we study the covariance of the anomalies. The x-axis is day of

year. With the upwelling signal (seen in A and B) removed, other patterns (seen in C and D)

emerge to represent most of the covariation.

Without effectively removing the seasonality, the first mode of variation, upwelling (see Figure

1.8 A and B) accounts for 47% of the variation. It demonstrates a strong but opposite

covariance: when upwelling winds are strongest (making the Wind Index most negative), NPP is

concentrated north of the cape (with the NPP Index most positive). By analyzing the anomalies

instead, thus removing the seasonal upwelling signal, the largest remaining signal (Figure 1.8 C

and D) accounts for 28% of the variation, but what it represents is far less clear.

However, examining the expansion coefficients (also known as time amplitudes), which is to say

how the strength of a given mode’s effect on the system varies in time, provides an opportunity

to identify mechanisms behind otherwise mysterious signals. And, with the mean removed, the

fifth-largest Empirical Orthogonal Function shown in Figure 1.9 (accounting for 10.8% of the

variability) has strikingly familiar-looking interannual variability in its time amplitudes.

22

Figure 1.9: The fifth modes of covariation (EOF5) for NPP (A) and Wind (B) in the case where

we analyze the system by removing the interannual mean/seasonality from each point. The x-

axis is day of year. C plots the expansion coefficients/time amplitudes for A, with the x-axis

now showing the 1-7 years of the analysis (2003-2009). D shows water year river discharge for

each of the same years.

There is a clear similarity between the time amplitude of EOF5 and the interannual variability of

Eel River discharge, with a maximum in water year 2005 and the sign of their derivatives

identical throughout the period analyzed. Correlation, of course, does not guarantee causation,

but it is possible that EOF5 is at least partially the signal of the river’s impact on coastal

variability.

1.13 Discussion and Conclusion

There is an abundance of research on the Eel River and the nearby Eel River Shelf, starting with

USGS gauging as early as 1910 and expanding in the 1980s and 1990s into full-scale research

programs of the shelf sedimentology (STRATAFORM) and the freshwater ecology of the river

itself (at the UC Angelo Coast Range Reserve). Using Net Primary Productivity values

estimated from MODIS ocean color data by Oregon State University, wind direction given by a

NOAA buoy near the mouth of the river, and USGS gauging to flag the times in which the Eel

River is significantly discharging its annual load, we can attempt to extract the possibly tiny

23

signal of short-term phytoplankton growth on Eel River storm-driven, nutrient-laden freshwater

plumes.

Granger causality indicates that to the extent that winds can predict NPP, they do so most

strongly during times of extreme Eel River R. discharge, and within that category, best during

the years of the largest storms, especially the 2005-2006 water year. Canonical correlation

analysis demonstrates that during upwelling season (as indicated by the NOAA upwelling

index), NPP is more strongly concentrated north of the cape than south of the cape. There are

many smaller modes of covariation between the two time series of winds and NPP, but the 5th

shows interannual variability similar to that of Eel River discharge, again most strongly

important to the overall system during the 2005-2006 water year.

Both Granger causality and CCA suggest that any direct connection between the NPP and wind

direction (proxy of Eel River nutrient delivery) time series is small. How reasonable is this? In

order to compare estimated magnitudes of Eel River discharge nutrient delivery to upwelling

nutrient delivery, let us consider a simple box model.

The mass continuity equation (in x-y-z three dimensional space, with velocities u, v, and w in the

respective directions) is

𝜕𝑢

𝜕𝑥+

𝜕𝑣

𝜕𝑦+

𝜕𝑤

𝜕𝑧= 0, (1)

but it can also be expressed per Bernoulli’s principle, such that for a continuous pipe of varying

width, the scalar component of the velocity times the area through which an inviscid fluid flows

is always constant:

𝑤1𝐴1 = 𝑤2𝐴2. (2)

This can be used to roughly estimate the rate at which upwelled, high-nutrient water enters the

system to replace surface waters drawn offshore by Ekman transport, as driven by a surface wind

stress, T.

24

Figure 1.10: A reference volume of mixed layer in the ocean. 𝑤1 is the horizontal velocity of

Ekman transport offshore, 𝑤2 is the upwelling velocity, �⃑� is the surface wind stress, L is a

reference length of coastline, D is the distance offshore, and H is the depth of the mixed layer.

Given a volume of the mixed layer in the ocean (as drawn in Figure 1.10), we can express that

water being transported offshore must be equally replaced by upwelling as:

𝑤1𝐴1 = 𝑤2𝐴2 (3)

𝑤1𝐿𝐻 = 𝑤2𝐿𝐷 (4)

𝑤1𝐻 = 𝑤2𝐷 (5)

𝑤1𝐻 is simply the Ekman Volume Transport, which can be estimated from a given surface wind

stress, water density ρ, and the Coriolis parameter f: 𝑤1𝐻 =�⃑�

𝜌𝑓. Upwelling is not constant

throughout its season, but time series of wind stress measurements have been taken over multiple

years of upwelling seasons in the northern California Current, with a seasonal average of 0.1

N/m2 (Bane et al. 2005), the density of water is 1000 kilograms per cubic meter, and at

midlatitudes the Coriolis parameter is approximately 10-4

s-1

; thus the Ekman Volume Transport,

and 𝑤1𝐻, is roughly equal to 1 m2/s. We now have estimates for the left hand side of equation 5,

and we want to solve for w2 on the right. Let D be 10 kilometers, as both a typical Rossby radius

(Pickett and Paduan 2003) and an estimate of how far offshore riverine nutrients might have an

effect, since we are trying to directly compare river delivery to upwelling in that same region of

interest. After the massive winter flood of January 1995, measurements in February and May

found the across-shore flood deposit to be 8 km wide (Wheatcroft et al. 1996). With this

estimate of D, a typical upwelling velocity is 𝑤2= 0.1 mm/s; a smaller D would increase this

value. The World Ocean Atlas gives a nitrate concentration of 40 micromoles per litre in this

region, at depths that will be upwelled to the surface (NOAA 2013c). This number may lack

representativeness to the Eel River deposit zone, as the World Ocean Atlas has a 1̊ horizontal

resolution. Now we can solve for the seasonal average upwelling transport rate of nitrate into the

region of interest:

𝑤2𝐴2[𝑁𝑂3−] = 𝑤2𝐷𝐿[𝑁𝑂3

−] = 107𝐿𝑖𝑡𝑟𝑒𝑠

𝑠𝑒𝑐𝑜𝑛𝑑∗ 40

𝑢𝑚𝑜𝑙

𝐿𝑖𝑡𝑟𝑒= 4𝑒8

𝑢𝑚𝑜𝑙

𝑠𝑒𝑐𝑜𝑛𝑑

(6)

25

According to USGS gauging at Scotia (USGS 2012), between 2002-2010, daily Eel River

discharge is above 5000 cubic feet per second, or 1.4e5 litres per second, 33.4% of the time; an

average of four months each year. This threshold is useful, as below 5000 cubic feet per second

discharge declines rapidly towards summer low-flow values. When flow is at or above this

threshold in the 2002-2010 period, the average discharge is about 20,000 cubic feet per

second/5.6e6 litres per second. Eel River nitrate concentrations in these winter months are often

8 micromoles per litre (USGS 2012; Figure 2.20), although it’s worth noting that measured

variability in the flood months can range over an order of magnitude in either direction, and a

more representative average is 3 micromoles per litre; the higher value of 8 is selected in order to

account for the probability of leeching effects during peak flow. Thus during winter, the Eel

River might be delivering 4.4e7 micromoles of nitrate per second, an order of magnitude less

than the rate of delivery during upwelling. When one considers that upwelling occurs over many

months of the year (see Figure 1.3; from 2002-2010 upwelling season varies between 5-8 months

in duration) and high flow is only for about 4 months, the difference in total annual nutrient

delivery only widens. Of course, these two signals, upwelling nutrient delivery and riverine

nutrient delivery, are out of phase, with summer upwelling and winter river flow. However, this

analysis also overlooks the presence of riverine particulate nitrogen, and its potential uptake both

upon delivery to the coastal ocean or after it has sunk (which could contribute to the nutrient

supply during upwelling season), which could create linkages between the two seasons’ coastal

ocean productivity in a delayed mechanism.

Still, the difference in magnitude cannot be overlooked. It is thus not surprising that it is difficult

to find first-order evidence of correlation between Eel River flow and primary productivity. If

the Eel River nutrients are having an immediate impact on the coastal ocean, the signal is tiny.

Still, based on the Granger causality and Canonical Correlation analyses, tiny indications exist –

although they’re well below the threshold of significance on an interannual timescale, it seems

possible that a small signal that peaks during moments in 2005 (the year with the highest flow in

the 2002-2010 period) might be related to the Eel River.

While the Eel River discharge/buoy wind measurement/NPP analysis does not get at longer-term

lags (such as the possibility of iron deposition by the river taking a year or two to sink, become

anoxic, and reduce, per the shelf capacitor hypothesis of (Chase 2007)), it demonstrates the

possibility of further studying these short-term connections with temporally and spatially high-

resolution modeling. A coupled modeling system that links hydrology and ocean circulation

beneath a unified atmosphere, in a single framework would be a potentially useful tool to explore

the importance of mountainous river discharge on the coastal ocean at timescales from hours to

years. For the case of the Eel River, a focus on water year 2005-2006, with the most extreme

storms of the decade (and the strongest indication of correlation, in both Granger and Canonical

Correlation Analysis), is likely to have the strongest signal and produce the most interesting

results.

26

Table 1.3: 2000-present Eel River papers by topic. Literature reviews and other particularly

useful papers are highlighted. Internal watershed dynamic literature is excluded.

Topic Authors Year Relevant details Significant results

Biogeochemical

cycling: anaerobic

conditions

Levin et al. 2000 Metazoan microfauna

from methane-seep

sediments on the

continental slope

Biogeochemical

cycling: anaerobic

conditions

Hinrichs et

al.

2000 Molecular and isotopic

analysis of anaerobic

methane-oxidizing

communities in marine

sediments

Biogeochemical

cycling: anaerobic

conditions

Rathburn et

al.

2000 As Hinrichs et al.

Biogeochemical

cycling: anaerobic

conditions

Levin and

Michener

2002 Stable isotope study at

the Eel R. margin:

Primarily sulfide-

oxidizing bacteria,

distinct microhabitats of

microbial mats

Methane bubbles emanating

from sediments beneath the

mats

Biogeochemical

cycling: anaerobic

conditions

Levin et al. 2003 Further study of

microbial mats

No oxygen could penetrate the

mats; Oxygen can penetrate

sediments down to 3-4 mm

Biogeochemical

cycling: anaerobic

conditions

Orphan et al. 2004 Overview of geological,

geochemical and

microbiological

heterogeneity of the

seafloor around methane

vents

Biogeochemical

cycling: anaerobic

conditions

Levin et al. 2010 Updated review on

methane vent

microbiology

Biogeochemical

cycling: anaerobic

conditions

Beal et al. 2009 Mn and Fe-dependent

marine methane

oxidation study on Eel

R. margin

Demonstrates that Fe and Mn

delivered in Eel R. sediments

can be used as electron

acceptors in marine anaerobic

oxidation of methane

Biogeochemical

cycling: anaerobic

conditions

Homoky et

al.

2009 Eel R. sedimentary Fe

redox cycling studied

through measurement of

isotopic iron in pore

fluids; Depth profiles of

nitrate, organic carbon,

mn and iron species

down to 20 cm depth

Results consistent with aerobic

respiration at the surface, with

dissimilatory iron reduction

starting at about 5 cm; evidence

for continuous reoxidation of

iron to amorphous

oxyhydroxides, with organic

carbon necessary for full

dissolution

27

Biogeochemical

cycling: anaerobic

conditions

Severmann et

al.

2010 Isotopically distinct

benthic iron flux

measured

They propose it’s remobilized

from the particulate by the

delivery of Eel R. reactive

organic carbon to the sea floor

by riverine discharge

Biogeochemical

cycling: anaerobic

conditions

McManus et

al.

2012 Benthic Mn fluxes from

the Eel R. continental

shelf an order of

magnitude higher than

other regional shelf

settings

Flux co-varies with the organic

carbon oxidation rate

Biogeochemical

cycling: anaerobic

conditions

Roy et al. 2013 Expansion on McManus

et al. 2012, studying Fe

and Mn fluxes from the

Eel R.

Found reactive iron and

manganese concentrations in

the Eel R. sediment positively

correlating with organic carbon

content

Biogeochemical

cycling: biological

perturbation of

shelf-held

sediments

Cutter and

Diaz

2000 Sediment profile and

surface image

examination for

biological alteration of

the physically structured

flood deposits

Mid-shelf deposits markedly

altered by polychaete burrows

Biogeochemical

cycling: biological

perturbation of

shelf-held

sediments

Sommerfield

et al.

2001 Comparison of

distributions of C, S, Fe

in both modern Eel

Sediments and ancient

mudrocks

Bioturbation intensity has been

constant for a very long time

Biogeochemical

cycling: biological

perturbation of

shelf-held

sediments

Richardson et

al.

2002 Evidence of large

burrowing that is

preferable for the

proliferation of sediment

biochemical reactions

Porosity turns out to be a good

way to resolve small-scale

biogenic variability

Biogeochemical

cycling:

characterization of

Eel R.-delivered

organic matter

Leithold and

Blair

2001 Carbon isotopic, C:N

and C:surface area ratios

of particles in Eel Flood

deposits expected to

reflect rapid unloading

of terrestrial carbon

from discharged

particles, but don’t

Possibly particle delivery to and

burial on continental shelf are

so rapid that kerogen is not

completely oxidized, and gets

recycled again

Biogeochemical

cycling:

characterization of

Eel R.-delivered

organic matter

Blair et al. 2003 As Leithold and Blair

2001, supported with

more data

28

Biogeochemical

cycling:

characterization of

Eel R.-delivered

organic matter

Leithold et

al.

2005 Isotopically

characterization and

analysis of wood

fragments from Eel

plume

Propose model for particulate

organic carbon transport and

burial

Biogeochemical

cycling:

characterization of

Eel R.-delivered

organic matter

Blair et al. 2004 Apply proposed model

to both Eel and Amazon

R.

Biogeochemical

cycling:

characterization of

Eel R.-delivered

organic matter

Locat et al. 2002 Characterization of 15

cm depth core samples

of sediment on the shelf

Organic matter on the order of

1-2% by mass; Whether OM

had been broken down post-

burial is unclear

Biogeochemical

cycling:

characterization of

Eel R.-delivered

organic matter

Drenzek et

al.

2009 A re-evaluation of the

importance of petrogenic

organic carbon burial in

marine sediments.

Particularly good

characterization of

organic matter and their

ages in Eel R. sediment

Previous assumption: vascular

plant detritus spends little time

sequestered in river deltas.

However: plants can be

sequestered for thousands of

years in soils before being

deposited as sediments!

Biogeochemical

cycling:

characterization of

Eel R.-delivered

organic matter

Goñi et al. 2013 Another thorough

characterization of Eel

R. particulate organic

matter delivered to the

ocean; Includes samples

from low and high flow

regimes

Sediment fate and

transport: physical

characterization

Friedrichs et

al.

2000 Bottom-boundary-layer

velocity profile study

Fine sediment accumulates even

in energetic environments like

the eel if it dominates the source

material and is abundant

Sediment fate and

transport: physical

characterization

Crocket and

Nittrouer

2004 Characterized sandy

fraction of sediment

50% accumulates on inner

continental shelf

Sediment fate and

transport: physical

characterization

Mullenbach

et al.

2004 Characterization of

sediment

12% of sediment accounted for

in upper Eel River Canyon

Sediment fate and

transport: physical

characterization

Mullenbach

and Nittrouer

2006 Isotopic (be, th, pb)

characterization of eel

river canyon sediment

2% is accumulating rather than

merely passing through

Sediment fate and

transport: physical

characterization

Hill et al. 2000 Settling velocities of

suspended sediment in

Eel River flood plume

During periods of extreme

sediment, heavy flocs form and

sink faster; there is both

widespread dispersal of flood

sediment off the shelf, and a

consistent locus of deposition of

flood layers on the shelf

29

Sediment fate and

transport: physical

characterization

Curren et al. 2002 Tested Hill et al.

hypothesis, found no

sediment between floc

size/concentration

Found relationship between

bulk mean settling velocity of

plume sediments, and wind

speed/direction

Sediment fate and

transport: gravity

flows

Geyer et al. 2000 Eel river storm plume

data (1996-1998)

There must be a mechanism

other than plume transport

delivering sediment from inner

shelf to midshelf

Sediment fate and

transport: gravity

flows

Traykovski et

al.

2000 Acoustic backscatter

data, water velocity

profiles during

depositional events

Proposed mechanism: density-

driven fluid mud flows

Sediment fate and

transport: gravity

flows

Ogston et al. 2000 Bottom boundary layer

tripods found near-bed

layer of suspended

sediment consistent with

fluid mud

Two-stage conceptual model,

plume sediment initially trapped

on inner shelf, then transported

seaward due to gravitational

forcing

Sediment fate and

transport: gravity

flows

Puig et al. 2003 Same group… Tested

model with 1999-2000

data

Found that storms can

resuspend older sediments into

fluid muds, delayed transport

mechanism much more

independent from the sediment

delivery in any single plume,

happens much more often than

thought possible

Sediment fate and

transport: gravity

flows

Ogston et al. 2004 Longer, superior

analysis of currents and

suspended-sediment

transport

Nearbed oscillatory flows and

mesoscale eddies help

determine transport along and

across the shelf

Sediment fate and

transport: gravity

flows

Guerra et al. 2006 Update of Ogston et al.

2004 analysis with more

details

Argue that secondary processes

both dominate and make the

inner shelf a line source of

sediment nourishing the mid-

shelf deposit (as opposed to a

point source at the Eel River

mouth)

Sediment fate and

transport: gravity

flows

Mullenbach

and Nittrouer

2000 Isotopic analysis of

1997-1998 sediment

cores

Storm resuspension and

transport of older sediments is

indicated

Sediment fate and

transport: gravity

flows

Wright et al. 2001 Capstone review of the

papers from 2000:

collects evidence for

gravity-driven sediment

resuspension and

transport into a more

coherent whole

30

Sediment fate and

transport: gravity

flows

Scully et al. 2002 Analytical modeling of

down-slope sediment

transport and deposition

by gravity-driven, wave-

supported flows

Success in reproducing

strataform time series of

velocity and deposition is strong

evidence for wave-supported

gravity flows controlling Eel R.

margin flood deposit

Sediment fate and

transport: gravity

flows

Wright et al. 2002 Analytical modeling to

study pulsational timing

of gravity-driven

transport

Sediment fate and

transport: gravity

flows

Friedrichs

and Wright

2004 Further development of

analytical model to test

across multiple

continental margins

Sediment fate and

transport: gravity

flows

Scully et al. 2003 Two-dimensional

numerical model of

wave-supported

sediment gravity flows

When river delivers sufficient

sediment to critically stratify

wave boundary layer, wave

intensity and Eel River shelf

bathymetry dominate deposition

pattern

Sediment fate and

transport: gravity

flows

Harris et al. 2005 Three-dimensional

hydrodynamic model of

sediment transport

mechanisms

Results indicate sensitivity to

the specific settling properties

of fine-grained sediment

Sediment fate and

transport: gravity

flows

Wright and

Friedrichs

2007 Major literature review

of gravity-driven

sediment transport

Sediment fate and

transport: gravity

flows

Kniskern et

al.

2011 New analysis of

discharge, wave, wind

conditions to create

gravity flows; compares

Eel R. to other western

US rivers

Excellent summary of available

Eel River sediment data

Sediment fate and

transport: gravity

flows

Warrick et al. 2013 Systematic multi-year

changes in Eel River

sediment concentration

are described

Sediment rating curve

calculations are found to be

highly sensitive to the

nonstationarity of the sediment

time series. Concern is raised

that this causes an

overestimation in previous

source-to-sink sediment budgets

on all time scales.

Sediment fate and

transport: gravity

flows

Warrick 2014 Eel River sediment

discharge rate estimation

is found to be

overestimated by a

factor of two

A new estimate that uses a time-

dependent sediment rating

curve accounts for most of the

difference between this study

and previous efforts.

31

Sediment fate and

transport:

sequence

stratigraphy and

climate change

Sommerfield

et al.

2002 Examination of

stratigraphic

preservation of flood

events and net

sedimentation rate

Stark increase in marine

sedimentation in recent decades

is a response to documented

climactic phenomena

Sediment fate and

transport:

sequence

stratigraphy and

climate change

Leithold et

al.

2005 Direct counterargument

to Sommerfield et al.:

land use > climate

change

Sediment fate and

transport:

sequence

stratigraphy and

climate change

Wheatcroft

and Drake

2003 Intense biological

mixing intensity on Eel

R. shelf dissipates

signals between 3-15

years

Except for episodic

sedimentation from Eel. R flood

events, which preserve event

beds and transient signals

Sediment fate and

transport:

sequence

stratigraphy and

climate change

Bentley and

Nittrouer

2003 As Wheatcroft and

Drake 2003, expanded.

Sediment fate and

transport:

sequence

stratigraphy and

climate change

Sommerfield

and

Wheatcroft

2007 Stratigraphic

preservation of flood

events study

Evidence of up to 1000-year-old

Eel R. flood events

Sediment fate and

transport:

sequence

stratigraphy and

climate change

Wheatcroft

and

Sommerfield

2005 Study of other Pacific

Northwest sediment

sources and sinks

Eel R.’s dispersal system

uniquely exhibits much greater

off-shelf transport than other

rivers in the region

Sediment fate and

transport:

sequence

stratigraphy and

climate change

Nittrouer et

al.

2007 Book: From Sediment

Transport to Sequence

Stratigraphy

Good summary of previous

research on sequence

stratigraphy

Sediment fate and

transport:

sequence

stratigraphy and

climate change

Andrews and

Antweiler

2012 A review of the

influences of climate,

geology and topography

on the sediment fluxes

of coastal California

rivers.

Climate change is found to be

potentially important.

32

Modeling efforts:

3D ocean

circulation

Pullen and

Allen

2000 Purely Physical 3D

model at 1 km resolution

using POM; 40 day

simulation.

Coastline irregularities

important to generating local

eddies, mixing of freshwater

plume influences velocity

structure of shelf flow

Modeling efforts:

3D ocean

circulation

Pullen and

Allen

2001 3 km and 9 km

resolution runs; Strong

alongshore variability in

wintertime flow, good

reproduction

Robust anticyclonic eddy forms

when strong poleward winds

weaken and reverse direction

during winter storms

33

Chapter 2: Methodology

2.1 Introduction and Literature Review: Previous Relevant Modeling Efforts

2.2 Modeling Framework Overview

2.3 Atmospheric Forcing

2.3.1 NARR

2.3.2 Bulk flux approximations in ROMS, 10 km horizontal resolution

2.3.3 ERA-Interim

2.3.4 Comparison: ERA-Interim vs. NARR, regional scale

2.3.5 Comparison: ERA-Interim vs. NARR vs. Daymet data, local scale

2.4 Hydrological Modeling: HydroTrend

2.4.1 HydroTrend Description

2.4.2 HydroTrend Discharge

2.4.3 HydroTrend Sediment

2.4.4 HydroTrend Parameterization

2.5 Ocean Modeling: Regional Ocean Modeling System

2.5.1 Equations of Motion

2.5.2 Curvilinear Coordinates

2.5.3 Vertical Coordinates

2.5.4 Domain and Grid Resolution

2.5.5 Bathymetry

2.5.6 Temporal Resolution and Numerics

2.5.7 Horizontal Diffusion and Viscosity

2.5.8 Vertical Mixing Parameterization

2.5.9 Boundary Conditions

2.5.9.1 Lateral Boundary Conditions

2.5.9.2 Bottom Boundary Conditions

2.5.10 Surface Model Forcing

2.5.11 River Forcing

2.5.12 Model Initialization and Spinup

2.6 Biogeochemical Modeling: Nutrient-Phytoplankton-Zooplankton-Detritus

2.6.1 NPZD description and limitations

2.6.2 NPZD ROMS dynamics

2.6.3 NPZD initial and boundary conditions

2.6.4 NPZD riverine input

2.7 Model Experimental Design

2.8 Model Results

2.8.1 Results: HydroTrend

2.8.2 Results: ROMS, 10 km resolution

2.8.2.1 Climatological validation

2.8.2.2 Short timescale validation


2.9 Conclusion

34

2.1 Introduction and Literature Review: Previous Relevant Modeling Efforts

Rivers are mostly absent from global climate modeling efforts. Although river and groundwater

runoff into the ocean is a driver of ocean models by land models, rivers themselves are usually at

the scale of subgrid variability, often parameterized as simply as a quantity of water and a

direction of flow. For example, in the Community Earth System Model (Gent et al. 2011), the

River Transport Model (Branstetter 2001, Branstetter and Famiglietti 1999) uses a linear

transport scheme at 0.5̊ resolution to route water from each grid cell to its downstream

neighboring grid cell, split into liquid and ice streams. They provide a freshwater flux to the

ocean, and their main function is to provide closure to the water cycle. The potential importance

of river effects on the land surface and coastal ocean is not significantly studied with this current,

simple scheme. Similarly, GFDL’s CM2 (Delworth et al. 2006) is simple in its treatment of

rivers: river flow into the ocean is based upon a predetermined river drainage map that collects

and routes runoff into the top 40m of the ocean, as a freshwater flux that instantly prescribes the

temperature as the same as the sea surface (which causes a heat sink). Does this gap need to be

addressed by improving the internal river modeling of global climate models? One way to

approach this question is to construct a regional-scale earth system modeling framework that

studies a specific basin/coastal ocean system. And at the regional scale, there is a long history of

modeling efforts to draw upon.

There have been a variety of previous modeling efforts especially relevant to this study. Perhaps

first among equals is the River Influences on Shelf Ecosystems program (Hickey et al. 2010)

which combined extensive sampling of the Columbia River plume with a major modeling effort.

They found that most plume nitrate originated from upwelled shelf water, and that there was no

significance difference in phytoplankton species carried within the plume and found in the

adjacent coastal ocean. The program used the Regional Ocean Modeling System (ROMS) to

perform a 3-month hindcast of 2004 summertime circulation on the Washington and Oregon

shelf, and within the Columbia River estuary (MacCready et al. 2009), with 20 vertical levels

and a 51.75s baroclinic time step, constrained by the speed of surface ebb currents at the

Columbia River mouth. They used USGS data for river flow and temperature, but did not model

the river directly. The same hindcast was performed with an unstructured grid called SELFE

(Zhang and Baptista 2008), which performed an analysis of the sensitivity of the plume to the

choice of the vertical grid. The ROMS results were used offline to drive a particle tracking

experiment (Banas et al. 2009a), which found that the Columbia plume seems to increase cross-

shelf dispersion by about 25% when it is present. The ecosystem used in RISE was an NPZD

four box model (Banas et al. 2009b), which was successfully implemented offline from ROMS

and used to analyze the effect of the presence of the plume on local coastal biology. Although

primarily studying the influence of El Niño, Columbia River flow was also included in a basin-

scale model of the north Pacific that ran from 1996-2002 (Hermann et al. 2009). It was found to

dominate anomalies of sea surface height in its region.

Nor is the Columbia Estuary the only application of ROMS to a river-ocean interface.

Numerical simulations of the Hudson River estuary have been performed (Warner et al. 2005)

that were able to capture large observed variations in stratification between neap and spring

tides, though without solid reproduction of the vertical salinity structure. The Chesapeake Bay

estuary has also been the study of a series of ROMS studies including (Li et al. 2005), which

35

analyzed the effect of differing turbulence closure schemes on the model results and found little

difference. However, the salinity stratification in this case was found to be very sensitive to the

background diffusivity, which is in turn strongly determined by the surface and bottom boundary

layer representations. ROMS was also applied to the Delaware Bay estuary (Castellano and

Kirby 2011) and demonstrated reasonable skill in predicting its hydrodynamic processes, but was

driven by an immense amount of local data. Other worldwide river plumes simulated

numerically from gauging data include the Mekong Delta (Hordior et al. 2006), Plata River

(Pimenta et al. 2005), and Brisbane River (Yu et al. 2011). Spaulding et al. (2010) collects many

of these efforts in one place for review.

The Eel River plume itself was modeled in a 1 km resolution, 40-day simulation of the

December 30, 1996 – January 3, 1997 flood event (Pullen and Allen 2000). The Naval Research

Laboratory’s Pacific West Coast Model, an implementation of the Princeton Ocean Model, was

used for this effort. A 100-day simulation at 4 km resolution (Pullen and Allen 2001) found

strong variability and complex flow even in the absence of river run-off, and reported a robust

anticyclonic eddy centered off the Eel River mouth that occurred in response to the transient

wind forcing imposed by passing storms. This was a purely physical modeling effort, but an

excellent demonstration of the usefulness of physically distributed numerical model applications

to the region.

In 2006, ROMS was used at 15 km resolution with a nested 5 km grid, to drive an eddy-resolving

plankton ecosystem California current model (Gruber et al. 2006). The model underestimated

phytoplankton in the northern part of the domain. Gruber et al. theorized that this was due to the

lack of short-term variations in the atmospheric forcing, though it is also true that coastal runoff

was neglected. Importantly, they attempted to model a variable chlorophyll:carbon ratio. In the

same region, the importance of coastal wind forcing to the ability of a model like ROMS to

capture upwelling was analyzed (Capet et al. 2004), and they found that present wind analyses

such as COAMPS do not adequately determine the most important wind properties, the strength

of the nearshore curl and the speed drop-off near the coast. Further study and comparison of the

strengths and weaknesses of wind fields such as QuickSCAT and the NCEP/NCAR reanalysis,

as used to drive eddy-resolving simulations of the Pacific, found that satellite wind fields with

small scale structures outperform reanalyses in high-resolution ocean simulations (Sasaki et al.

2006).

While there have been numerous modeling efforts to resolve river plumes (Spaulding et al.

2010), and equally numerous modeling efforts to resolve planktonic dynamics in the coastal

ocean (Franks 2002), there have been very few that unify these two interests by using a modeled

watershed rather than existing river gauging data. In order to test how well models can study the

biological effects of riverine input to the coastal ocean, and as a first step to the possible

inclusion of such an earth system modeling framework within the larger climate models, a test

case is useful: the Eel River, with its dramatic behavior summarized in Chapter 1, is an obvious

choice.

36

2.2 Modeling Framework Overview

In the coupled modeling framework (Fig. 2.1), the watershed is represented with the lumped

empirical hydrology model HydroTrend (Kettner and Syvitski 2008; Section 2.4), which can

generate high-frequency water and sediment time series. HydroTrend was selected due to its

modest prior success at modeling the Eel River as a test case (Syvitski et al. 1998a), and its

ability to be driven by the same atmospheric input as the ocean model, thus creating a unified

earth system modeling framework. The ocean is represented with the Regional Ocean Modeling

System (ROMS; Shchepetkin and McWilliams 2005; Section 2.5), a powerful, modular,

physically distributed ocean circulation model that can efficiently solve the primitive equations

on the rotating Earth for momentum, heat, and other tracers, on fine-scale resolution grids.

ROMS is used at two horizontal resolutions: 10 km and 1 km. Transforming HydroTrend’s

output into a form suitable to force the ocean and biology (Section 2.6) models requires a

coupling interface based on the generation of a three-dimensional, nutrient-laden freshwater

plume (Sections 2.5.11 and 2.6.4). The atmosphere (Section 2.3) is represented in the 10 km

horizontal resolution experiments with the NCEP North American Regional Reanalysis (NARR;

Mesinger et al. 2006), a model and data assimilation tool. For the 1 km resolution model, due to

the poor performance of NARR at fine scales using a bulk flux approximation, the ERA-Interim

reanalysis data assimilation system (Dee et al. 2011) was used for atmospheric forcing instead.

The Eel River was modeled in HydroTrend from 1979-2010. The coastal ocean was modeled in

ROMS from 2000-2010 with 10 km horizontal resolution, without inclusion of the river or

biology. A nested 1 km resolution model was run from 2002-2010, and carried within it the

Nutrient-Phytoplankton-Zooplankton-Detritus biological model (Powell et al. 2006; Section 2.6),

as well as the physical and biological presence of the Eel River. Model experimental design is

discussed in Section 2.7, while model results are discussed in Section 2.8.

The 10 km ROMS runs were computed on 64 parallel processors of the Hadley Computing

Cluster at Lawrence Berkeley National Laboratory. The 1 km ROMS runs were computed on

256 parallel processors of the Yellowstone High-Performance Computing Cluster at the National

Center for Atmospheric Research (CISL 2014).

37

Figure 2.1: The coupled modeling framework.

2.3 Atmospheric Forcing

The choice of atmospheric forcing is critical to the land surface and ocean models – and the

choice to use the same dataset for both models is ultimately what closes the circle of the

modeling framework. Initially, the North American Regional Reanalysis was selected for its

high resolution both temporally and spatially. However, in order to apply NARR to ROMS, bulk

flux approximations were necessary, and the inadequacy of these approximations under

conditions of low winds, particularly at 1 km horizontal resolution in ROMS, led to the search

for an alternative atmosphere.

Use of the ERA-Interim dataset is a compromise. Its horizontal resolution is nearly an order of

magnitude inferior to NARR, but its fields allow direct application of surface stress, as well as

heat and water fluxes, onto and across the sea surface boundary. The use of ERA-Interim on 1

km ROMS significantly reduced sea surface temperature, which had previously been running

several degrees too hot. However, the 10 km ROMS results were not rerun with ERA-Interim

atmosphere due to the constraint of computational expense, so the influence of NARR and the

bulk flux approximations remain in the initialization and boundary conditions of the 1 km

results.

The difference between NARR and ERA-Interim atmospheres in HydroTrend is explored in

section 2.3.5.

38

2.3.1 NARR

The North American Regional Reanalysis (Mesinger et al. 2006) is a long-term, consistent, high

resolution climate dataset for the North American domain in both atmospheric and land surface

hydrology. It spans 1979-present on a 32 km horizontal resolution and 38 vertical levels of

pressure in the atmosphere. Sea surface temperatures were derived from the 1̊ Reynolds dataset

(Reynolds et al. 2002). Notably, NARR 10 m winds have a slight negative bias in both winter

and summer, while NARR’s residual of the atmospheric water balance shows a significantly

positive bias (due to excess precipitation) along much of the Northwest coast of CONUS,

starting at roughly Cape Mendocino (Mesinger et al. 2006).

2.3.2 Bulk flux approximations in ROMS, 10 km horizontal resolution

The bulk flux approximations used in ROMS model an ocean-atmosphere boundary layer using

air-sea exchange parameterizations from Liu et al. (1979). NARR provides surface U-wind

(positive Eastward) and V-wind (positive Northward) components (m/s), air temperature (C),

pressure (mb), relative humidity (%), cloud fraction (0 to 1), rainfall rate (kg/m2/s) and

shortwave radiation flux (W/m2). As described in Liu et al. (1979), Monin-Obukhov similarity

theory is then used to estimate the turbulent fluxes for wind, heat and moisture. However, the

basic similarity profile assumption that the roughness length is much smaller than the Monin-

Obukhov length is violated at wind speeds below about 0.5 m/s, a condition that occurs regularly

in this system. For this reason, use of the bulk flux boundary layer was abandoned at the 1 km

horizontal scale. At 1 km, the change in atmospheric boundary forcing accounted for

approximately 2̊ Celsius of extraneous sea surface temperature, particularly in summer.

2.3.3 ERA-Interim

ERA-Interim (Dee et al. 2011) is the latest global atmospheric reanalysis produced by the

European Centre for Medium-Range Weather Forecasts (ECMWF). It covers 1979-present on a

0.75-1.125 ̊ resolution horizontal grid, and uses a powerful 4-dimensional variational

assimilation, as well as variational bias correction of satellite radiance data, and more extensive

use of radiances with an improved fast radiative transfer model (Dee et al. 2011). Both 3-hour

and 6-hourly surface parameters are available, within the 12-hourly analysis cycle of the

sequential data assimilation scheme. In each cycle, available observations are combined with

prior information from a forecast model to estimate the evolving state of the atmosphere and its

underlying surface (Dee et al. 2011). Outputs include direct boundary conditions for ROMS:

surface stress in the u and v directions, and fluxes of heat and moisture (for more information,

see section 2.5.10). Excessive solar radiation in ERA-Interim causes a net heat flux into the

ocean, but this bias is mostly concentrated in convective tropical areas; if anything the ocean is

up to a degree too cold in our region of interest, while land surface temperatures average out

within a degree in either direction depending on the time of year (Stopa and Cheung 2014).

Wind speeds are slightly underestimated, but ERA-Interim’s consistency through time (as

opposed to carrying a large spin-up or spin-down bias) makes it especially useful for multi-year

forcing and intercomparison (Stopa and Cheung 2014).

39

2.3.4 Comparison: ERA-Interim vs. NARR, regional scale

In order to understand differences introduced to the modeling framework by use of either of

these atmospheric forcings, Figures 2.2 to 2.9 show comparisons of monthly climatologies

(1985-2010) between ERA-Interim and NARR datasets for precipitation (12-hourly),

temperature (6-hourly) and winds (6-hourly), for the months of January (when Eel storm events

are important) and July (when upwelling is important), as both a spatial map and a histogram of

the values that went into the map. In January (Figure 2.2), we see that NARR is wetter than

ERA-Interim on the order of 3 mm/day, throughout much of the Eel River watershed. This

highlights the misleading outcome of only looking at precipitation near Eureka and the mouth,

since such a comparison shows ERA-Interim having heavier precipitation, on average. Over the

ocean, NARR is 1-2 mm/day dryer than ERA-Interim. Nonparametrically, we see that NARR is

generally more extreme than ERA-Interim, reaching greater maximum precipitation and a large

region of minimal precipitation as well (which is over the ocean). In July (Figure 2.3), all

precipitation is an order of magnitude less than in January, and the differences between datasets

are similarly smaller, though in the same direction as January. For 2 m height air temperature in

January (Figure 2.4), the datasets are essentially identical over the ocean but vary in isolated

patches over land, with NARR 2-3̊ warmer than ERA-Interim throughout most of the Eel

Watershed. The histograms are quite similar. In July (Figure 2.5), temperature over the ocean is

again nearly identical, with a slight warming bias in NARR onshore. Over land, ERA-Interim is

2-3̊ warmer north of Eureka, and then steadily cooler as one progresses south past San Francisco.

NARR reaches greater maxima of heat, but ERA temperatures are more widely distributed across

the temperature range.

Given basin-averaged temperature and precipitation for HydroTrend, the net effect we would

expect is more river discharge from NARR (since there is consistently more precipitation) offset

to some degree by greater evaporation (since overland temperatures are higher), and less

snowfall (since NARR is typically warmer) leading to a more continuous, less snowmelt-driven

discharge rate in winter. In ROMS, the cooler, dryer ocean surface forcing of NARR would be

expected to inhibit heat flux out of the ocean, while encouraging a net increase in water flux

(generally defined as Evaporation – Precipitation), though the relative magnitude of NARR-

driven versus ERA-driven evaporation would be moderately smaller due to the cooler air.

The histograms are especially useful for interpreting differences in NARR and ERA winds, as

they can be negative, and the result of their direct subtraction can obfuscate issues related to their

sign. Winds in the U (positive East, negative West) direction are similar over the ocean in

January (Figure 2.6), with a trend towards stronger NARR winds over the ocean as one

progresses south of Cape Mendocino. The NARR U-wind distribution is centered more

positively than ERA, on the order of 0.5 m/s overall, 1-2 m/s overland and near the mouth of the

Eel, which could have the effect of pushing Eel storm plumes onshore more strongly than ERA-

Interim. V-winds (positive North, negative South), which drive coastal upwelling and are crucial

during storm periods, are perhaps the most important of these four variables to compare. In

January (Figure 2.8), the NARR winds are consistently stronger (and more positive/northward),

with an exception: right at the mouth of the Eel River, heading north where the Eel storm plumes

are often thought to be advected (Wheatcroft et al. 1997), ERA-Interim is about 0.5-1 m/s

40

stronger than NARR. Over land, NARR has consistently stronger southerly winds, often 3 m/s

compared to ERA’s more typical 1 m/s.

In July (Figure 2.7), NARR U-winds are consistently 1 m/s stronger than ERA-winds offshore,

but onshore, in the upwelling zone, that bias weakens, nearing zero with any small positive bias

going to ERA-Interim, instead. Over land, the two datasets remain similar in the Eel watershed,

with small geographical patches of both NARR and ERA bias further south. In V-winds (Figure

2.9), the contrast is noticeable: NARR has consistently weaker upwelling winds north of Cape

Mendocino, starting at 1 m/s weaker and going up to 2.5 m/s in the extrema, while this bias

reduces along the coast, nearing zero south of Cape Mendocino. On shore, the northerlies are up

to 4 m/s stronger in NARR, with a positive bias up to 4 m/s in ERA-Interim further inland.

The most significant wind differences in the atmospheric forcings are overland, which is

irrelevant to HydroTrend and masked off in the ROMS ocean model. However, ERA-Interim’s

stronger upwelling winds are likely to have a significant impact on the biological component of

the model during the summer season when the river is likely to be unimportant. In winter, ERA-

Interim’s slightly stronger southerlies near the mouth of the Eel River might have an impact on

the fate and transport of river plumes, while acted upon by a NARR atmosphere those plumes

might have been driven closer to shore by stronger U-winds.

For the purposes of the modeling framework, the most significant differences between the

atmospheric datasets appear to come from precipitation (NARR being wetter than ERA-Interim

during the storm season) and V-winds (ERA-Interim having stronger upwelling winds than

NARR, and ERA-Interim having slightly stronger southerlies near the mouth of the Eel River

during the winter). The temperature biases are markedly large, but they occur mercifully outside

of our domain of interest.

41

Figure 2.2: 1985-2010 January climatology of precipitation, ERA-Interim subtracted from

NARR (top) and histogram comparing precipitation spatial distributions (bottom).

42

.

Figure 2.3: 1985-2010 July climatology of precipitation, ERA-Interim subtracted from NARR

(top) and histogram comparing precipitation spatial distributions (bottom).

43

Figure 2.4: 1985-2010 January climatology of temperature, ERA-Interim subtracted from NARR

(top) and histogram comparing temperature spatial distributions (bottom).

44

Figure 2.5: 1985-2010 July climatology of temperature, ERA-Interim subtracted from NARR

(top) and histogram comparing temperature spatial distributions (bottom).

45

Figure 2.6: 1985-2010 January climatology of U (positive Eastward) winds, ERA-Interim

subtracted from NARR (top) and histogram comparing spatial wind distributions (bottom).

46

Figure 2.7: 1985-2010 July climatology of U (positive Eastward) winds, ERA-Interim subtracted

from NARR (top) and histogram comparing spatial wind distributions (bottom).

47

Figure 2.8: 1985-2010 January climatology of V (positive Northward) winds, ERA-Interim


48

Figure 2.9: 1985-2010 July climatology of V (positive Northward) winds, ERA-Interim


49

2.3.5 Comparison: ERA-Interim vs. NARR vs. Daymet data, local scale

HydroTrend (see section 2.4) requires input of sea level temperature and basin averaged

precipitation. These can be delivered stochastically, by defining a set of climate parameters, or

directly with time series. With two sets of atmospheric forcing data available, basic comparisons

of these data to a ground truth is prudent.

The Daymet (Thornton et. al. 2014) data set (1 km horizontal resolution) provides gridded

estimates of weather parameters for North America, including continuous surfaces of minimum

and maximum temperature and precipitation occurrence and amount. Monthly climatologies

were constructed from 1985-2010 daily data spatially averaged from 40-42 N, -122 to -124 W,

an area that includes much of the Eel River Basin.

The North American Regional Reanalysis (32 km horizontal resolution) has three-hourly

estimated temperature and precipitation. The four overland points nearest the Eel River mouth

were averaged together to generate a time series for HydroTrend from 1979-2010. Climate

statistics were also calculated, for comparison to the on-the-ground data from the station.

The ERA-Interim Reanalysis (1.5̊ horizontal resolution) has six-hourly estimated temperature

and precipitation. The two overland points nearest the Eel River mouth were averaged together

to generate a time series for HydroTrend from 1998-2010 (and this difference in time coverage

may account for some of the differences we see), with climate statistics also generated.

In Figure 2.10 we see that the Daymet and NARR monthly average temperatures agree well,

with an earlier and shorter summer peak, and cooler winters, in Daymet. ERA fails to capture

the extremity of the seasonality, with smaller differences in average temperature throughout the

year. NARR's average temperature (11.27̊ C) is nearly a full degree warmer than Daymet's

average (10.4̊ C) while ERA is modestly cooler (10.15̊ C). Figure 2.11 demonstrates that both

the NARR (1342.32 mm) and ERA (1422.67 mm) annual average precipitation overestimate the

Daymet data (1244.93 mm) by up to 115%. The reanalyses tend to underestimate precipitation

in summer, and overestimate it in winter, but the differences are fairly small overall.

When compared to the within-month standard deviation of the Daymet data, the significance of

the difference between the datasets becomes clear: the difference in precipitation is insignificant,

while the difference in temperature is significant. Despite overestimating the Daymet

precipitation on average, NARR and ERA precipitation falls well within one standard deviation

of the Daymet data’s variability (Figures 2.13 and 2.15), presumably because of the extreme

behavior of winter storm events. The difference in temperature, however, is far greater than one

standard deviation, any given month of the year, for ERA, and diverges significantly for NARR

in the latter half of the year (Figures 2.12 and 2.14).

50

Figures 2.10 (top) and 2.11 (bottom): mean monthly temperature and precipitation for the

Daymet Dataset, the North American Regional Reanalysis, and ERA-Interim.

51

Figure 2.12: Comparison of the within-month standard deviation of Daymet temperature data to

the monthly average difference between Daymet data and the North American Regional

Reanalysis.

52

Figure 2.13: Comparison of the within-month standard deviation of Daymet precipitation data to

the monthly average difference between Daymet data and the North American Regional

Reanalysis.

53

Figure 2.14: Comparison of the within-month standard deviation of Daymet temperature data to

the monthly average difference between Daymet data and the ERA-Interim.

54

Figure 2.15: Comparison of the within-month standard deviation of Daymet precipitation data to

the monthly average difference between Daymet data and the ERA-Interim.

To summarize: Comparing the fields of temperature, precipitation and winds overall, NARR

appears to be wetter than ERA-Interim, with stronger winds, particularly upwelling winds.

However, ERA-Interim appears to have slightly stronger southerly winds near the mouth of the

Eel River during the winter. As compared to field data taken at the Eureka Weather Station,

however, while both NARR and ERA-Interim have substantially more precipitation, it is not

significant when compared to the extreme variability of the system’s storm events – while their

relative warmth in temperature does appear to fall outside of one standard deviation of the field

data. Because of the necessity of using ERA-Interim at 1 km in ROMS, HydroTrend must be

forced with it as well, in order for both parts of the framework to be acted upon by the same

atmosphere.

2.4 Hydrological Modeling: HydroTrend

2.4.1 HydroTrend Description

HydroTrend (Kettner and Syvitski 2008) is an empirical, lumped watershed model. Given basin

temperature, precipitation, hypsometry, relief, and qualities of the land surface parameterized for

evapotranspiration and groundwater and glacial storage and flow, it outputs daily time series of

water discharge and sediment load. Having been parameterized in HydroTrend1 (Syvitski et al.

1998) for use as an example, there was ample information available about how to parameterize

the Eel River basin for HydroTrend3 (Kettner and Syvitski 2008). The physical delivery of Eel

River discharge into the ocean circulation model ROMS is discussed in section 2.5.11, while the

biogeochemical delivery of Eel River-borne nutrients is described in section 2.6.4.

55

To summarize the key outputs here, HydroTrend generates total water discharge, Q, and total

sediment load Qsed = Qs + Qb, where Qs is suspended sediment and Qb is bedload sediment. The

calculation of Q and Qsed is discussed below.

2.4.2 HydroTrend Discharge

HydroTrend conceptually uses a simple water balance model of (P)recipitation per unit (A)rea,

reduced by (Ev)aporation and modified by water Storage and Release (Sr).

𝑄 = 𝐴 (𝑃𝑖 − 𝐸𝑣𝑖

𝑛

𝑖=1

± 𝑆𝑟𝑖) (7)

In HydroTrend’s calculations, the model simultaneously partitions water into five runoff

processes: rain (Qr), snowmelt (Qn), glacial melt (Qice), groundwater discharge (Qg) and

evaporation (Qev). For each month i in equation 7, the total annual discharge Q can be estimated

from:

𝑄 = 𝑄𝑟 + 𝑄𝑛 + 𝑄𝑖𝑐𝑒 − 𝑄𝐸𝑣 ± 𝑄𝑔 (8)

However, what ultimately defines daily discharge is the sum of surface runoff (qs) and

subsurface storm flow (qss), as visualized in Figure 2.16. It is these that we describe below.

Figure 2.16: Partitioning and transport within the water cycle, in HydroTrend 3.0.

Surface runoff qs: Pd is simply daily precipitation. The discharge due to rain, Qr, is reduced by

evaporation due to canopy interception (𝑒𝑐), and then by groundwater evapotranspiration (𝑒𝑔𝑤).

56

If the rainfall rate is greater than the canopy interception, then the amount of precipitation that

reaches the ground, Pg, is:

𝑃𝑔 = 𝛼𝑔 + 𝛽𝑔𝑃𝑑 𝑤ℎ𝑒𝑛 𝛼𝑔 + 𝛽𝑔𝑃𝑑 > 0

0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (9)

Where 𝛼𝑔 and 𝛽𝑔 are ground-precipitation coefficients (mm/d and unitless respectively)

(Sivapalan et al. 1996), with typical values of -0.1 mm/d and 0.8-0.9 respectively. Thus canopy

evaporation is simply the difference between total daily rainfall and what reaches the ground; all

canopy interception is assumed to evapotranspirate.

𝑒𝑐 = 𝑃𝑑 − 𝑃𝑔 (10)

From there, Pg must be partitioned into surface runoff and groundwater infiltration. The surface

runoff qs is equal to the sum of saturation excess runoff (qse) and infiltration excess (qie), all in

cubic meters per second:

𝑞𝑠 = 𝑞𝑠𝑒 + 𝑞𝑖𝑒 (11)

The saturation excess runoff (equation 12) is a function of how full the groundwater storage pool

is, and the rain rate, modified by 𝛼𝑐 and 𝛽𝑐, the unitless saturation excess coefficient and

exponent (Sivapalan et al. 1996), with typical values of 0.98 and 1.0 respectively. Maximum and

minimum levels of groundwater storage pools (in cubic meters) are given parameters, GWmax

and GWmin, while current amount of groundwater storage, GWstore, varies with each timestep:

𝑞𝑠𝑒 =

0 𝑤ℎ𝑒𝑛 𝐺𝑊𝑠𝑡𝑜𝑟𝑒 < 𝐺𝑊𝑚𝑖𝑛

𝛼𝑐 𝐺𝑊𝑠𝑡𝑜𝑟𝑒 − 𝐺𝑊𝑚𝑖𝑛

𝐺𝑊𝑚𝑎𝑥 − 𝐺𝑊𝑚𝑖𝑛 𝛽𝑐

𝑃𝑔 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒. (12)

The other component of surface runoff as defined in equation 11, infiltration excess qie, is simply

what remains of the precipitation rate that reaches the ground after the infiltration rate 𝑓𝑠 (mm/d)

and the saturation excess qse have been removed. Infiltration excess is constrained to be greater

than or equal to zero.

𝑞𝑖𝑒 = 0 𝑤ℎ𝑒𝑛 𝑃𝑔 − 𝑞𝑠𝑒 − 𝑓𝑠 ≤ 0

𝑃𝑔 − 𝑞𝑠𝑒 − 𝑓𝑠 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒. (13)

The method used to calculate fs, the groundwater infiltration rate, is dependent on precipitation

(equation 14).

𝑓𝑠 =

𝑃𝑔 𝐴𝑟𝑒𝑎 𝐶1 𝑤ℎ𝑒𝑛 𝑃𝑔 ≤ 𝑃𝑐𝑟

𝐾0 𝐴𝑟𝑒𝑎 𝐶1 𝑤ℎ𝑒𝑛 𝑃𝑔 ≥ 𝑃𝑚𝑎𝑥

𝐶1𝑃𝑔 𝐾0 − 𝑃𝑐𝑟𝑃𝑚𝑎𝑥 − 𝑃𝑐𝑟

𝐴𝑟𝑒𝑎 𝑤ℎ𝑒𝑛 𝑃𝑐𝑟 < 𝑃𝑔 < 𝑃𝑚𝑎𝑥

(14)

57

where C1 is a conversion constant and

𝐴𝑟𝑒𝑎 = 1 − 𝐺𝑊𝑠𝑡𝑜𝑟𝑒−𝐺𝑊𝑚𝑖𝑛

𝐺𝑊𝑚𝑎𝑥−𝐺𝑊𝑚𝑖𝑛 (15)

If the rain rate is less than a minimal infiltration rate (Pcr = 10 mm/d for the Eel River (Syvitski et

al. 1998)), then all of the rain will infiltrate, while when the rain rate is high enough (Pmax, 400

mm/d for the Eel River (Syvitski et al. 1998)) to force the maximum hydraulic conductivity (𝐾0

= 374.0 mm/d [Freeze 1974; Freeze and Cherry 1979]), then the infiltration rate reaches its

maximum, constant value. Between the two extremes, a linear fit estimates the infiltration rate

accordingly. Pmax is set to 400.0 mm/d based on previous calculations (Syvitski et al. 1998).

There is no strong justification in Syvitski et al. 1998 for these numbers; the largest recorded 24-

hour precipitation event measured at Eureka, CA was 172mm on December 27, 2002 (National

Weather Service 2014), and while Eureka is not representative of the entire basin, this huge

difference in magnitude suggests that modeled watershed conditions will never reach this

maximum value, creating a probable underestimation of the groundwater infiltration rate.

Subsurface storm flow qss: Having calculated qs by adding the results of (12) and (13), the

surface runoff term is now known. What remains is to estimate the contribution of groundwater

to river discharge, qss. In terms of the total amount of groundwater present during a given

timestep, GWstore, the groundwater pool for rainfall uses the previous calculations for infiltration

rate to fill itself, while a user-specified fraction of the daily total ice melt and snowmelt is

allocated to groundwater flow, made to lag a user-specified number of days behind the day that

caused the melt (see Table 2.1 for these parameters).

The discussion of ice and snowmelt in HydroTrend will be kept brief as these terms are fairly

small in the Eel River system. Snowfall is partitioned from total precipitation by estimating the

Freezing Level Altitude from the adiabatic lapse rate, and from there the fraction of the area

above the FLA (as defined by the hypsometric, height-per-area, curve for the Eel River

watershed) experiences snow instead of rain. Snow can be stored, or melt. This hypsometric

curve was calculated from the USGS National Elevation Dataset (USGS 2011).

Evapotranspiration from the groundwater pool is defined as

𝑒𝑔𝑤 = 𝛼𝑔𝑤 𝐺𝑊𝑠𝑡𝑜𝑟𝑒

𝐺𝑊𝑚𝑎𝑥 𝛽𝑔𝑤

(16)

where 𝛼𝑔𝑤 (10 mm/d) and 𝛽𝑔𝑤 (1, unitless) are the groundwater evaporation coefficient and

exponent respectively (Syvitski et al. 1998), dependent on the depth of the groundwater pool and

the type and abundance of vegetative cover. Finally, the subsurface storm flow qss (m3/s, from

groundwater to the river) is defined as

𝑞𝑠𝑠 = 𝛼𝑠𝑠 𝐺𝑊𝑠𝑡𝑜𝑟𝑒 − 𝐺𝑊𝑚𝑖𝑛

𝐺𝑊𝑚𝑎𝑥 − 𝐺𝑊𝑚𝑖𝑛 𝛽𝑠𝑠

(17)

58

where 𝛼𝑠𝑠 (700 m3/s) and 𝛽𝑠𝑠 (1.3, unitless) are subsurface storm-flow coefficient and exponent

set through curve fitting the discharge event after a rain event that is thought to be solely due to

groundwater discharge (Syvitski et al. 1998).

Thus what ultimately comprises Q, total river discharge, is the sum of (11) and (17).

2.4.3 HydroTrend Sediment

HydroTrend separately estimates suspended sediment load and bedload, the sum of which is used

to estimate Eel River remineralizable detritus delivery to the coastal ocean (in section 2.6.4).

Qsed = Qs + Qb (18)

Empirical relations that relate sediment load (Qs) to basin area, discharge, relief, temperature,

average basin lithology and human activity (BQART) were created for HydroTrend by analyzing

observational data of 340 rivers globally (Syvitski and Milliman 2007).

𝑄𝑠 = 𝜔𝐵𝑄 0.31𝐴0.5𝑅𝑇 (for 𝑇 ≥ 2 ℃) (19)

𝑄𝑠 = 𝜔𝐵𝑄 0.31𝐴0.5𝑅 (for 𝑇 < 2 ℃)

A, R, and 𝑄 are drainage basin area, maximum relief (calculated from the hypsometric curve)

and long-term average discharge respectively, the latter derived from a long-term average of the

Q calculated in section 2.4.2. 𝜔 is a constant of proportionality defined as 𝜔 = 0.02 kg/s/km/C.

T is basin averaged temperature (based on ERA-Interim, the atmospheric forcing, in this case), B

= L(1-Te)Eh, where Te is the trapping efficiency of a reservoir or lake, L is the lithology and Eh is

the anthropogenic factor. L ranges from 0.5 for basins comprised of hard, acid plutonic or high-

grade metamorphic rocks, up to 3 for basins having an abundance of exceptionally weak

material, such as crushed rock, loess deposits, or shifting sand dunes. The anthropogenic factor

Eh has methods of estimation described in Syvitski and Milliman (2007), typically ranging from

0.5 to 8. It can be higher given exceptional human impact on sediment, as with the Eel River’s

logging practices (Grant and Wolff 1991).

There are many reasons to be cautious in the use of sediment rating curves. One consideration is

the reliability of the accuracy of the data from which sediment rating curves are fit; while errors

in sediment load estimation can result from sample collection techniques and laboratory

procedures, the greatest errors appear to result from the inadequacy of a sampling program in

defining the detailed temporal record of suspended sediment concentration (Walling 1977a).

Walling (1977a) found it broadly worthwhile to use different curves for different seasons, and

for periods of rapidly increasing discharge (rising stage) and periods of declining river discharge

(falling stage); he notes that the concentration-streamflow relationship for individual storm

runoff events demonstrate a marked hysteretic effect, with concentrations for a given discharge

being considerably higher on the shorter-duration rising limb of a hydrograph. Even taking stage

and season into consideration, he found that annual loads could be overestimated by as much as

30%, and errors in estimation of monthly loads could vary between +900% and -80%. These

results refer specifically to instantaneous rating curves used in combination with hourly flow

data; different findings could result from the use of daily or annual rating curves. Thomas

59

(1988) also studies the effects of sampling methodology on the quality of rating curves. By sub-

sampling a large dataset in four different ways, in order to simulate different choices of when to

measure sediment in a river, he found systematically different patterns of sediment rating curve

position, and thus estimates of total suspended sediment yield.

Walling (1977b) tested his concerns pertaining to data collection frequency by using daily (rather

than hourly) mean flow data; he found underestimation errors of up to 50% for six east Devon

streams and three larger Devon rivers, with a tendency of the magnitude of the error to decrease

with increasing basin size. He considered three causes of scatter in the relationship between

sediment concentration or load, and water discharge: scatter related to inaccuracies of field and

laboratory measurements, scatter related to the dynamics of erosion and sediment yield, and

scattter resulting from marked non-stationarity of basin response to discharge. He considered the

second group the most important, but also proposed that on short timescales, the rating

relationships of individual storms might indicate the effect of successive storm depletion, with

sediment concentrations decreasing from one storm to the next. This non-stationarity effect

turned out to be very important for the case of the Eel River and other coastal northern California

rivers on much longer timescales (Warrick et al. 2013, Warrick 2014, see below).

A later study of sediment rating curves attempted a more theoretical approach to statistical

estimation of the bias in the use of linear least squares regression to estimate logarithms of

unmeasured concentration (Ferguson 1986). Linear least squares regression was shown to often

create a 50% underestimation of river loads no matter how intense the sampling; a bias

correction term was proposed that saw popular use (for example used in Thomas (1988), and

reviewed in Asselman [2000]). Thomas 1988 observes that the effect of this bias correction is

still dependent on sampling method and storm size, while Asselman (2000) abandons linear least

squares regression entirely (after reproducing the finding that rating curves created by these

measures underestimate long-term sediment transport rates by 10-50%), and found that he could

obtain better estimates using nonlinear least squares regression. He also expressed concern about

the potential lack of stationarity of rating coefficients, and the lack of means of judging that

stationarity at all. Horowitz (2003) again found that the sediment rating-curve method tends to

underpredict high suspended sediment concentrations, but furthermore overpredicts low

suspended sediment concentrations. Like Walling (1977a) and (1977b), he found that higher

temporal resolution of the estimates reduced the magnitude of the error, as did basing sampling

times on the ongoing hydrology (eg, rising and falling stage in Walling [1977a]) rather than

arbitrarily based on the calendar. He also found that using separate rating curves for each year

based on available data could improve the output.

For the specific case of the Eel River, Wheatcroft and Borgeld (2000) created sediment rating

curves that included the Ferguson (1986) bias correction and an unweighted least squares

method. By creating curves with and without 1) consideration of hysteresis, 2) consideration of

pre-1970 data, and 3) allowance of suspended sediment concentration unsupported by the data,

they saw that these choices changed the estimate considerably. Hysteresis was found to have

only a minor impact on the load estimates, but that they could remove seasonality as a potential

bias by using only data from the winter rainy season. However, this was still a technique that

used stationary coefficients, and non-stationarity was discovered to be critical to the system.

Warrick et al. (2013) showed that systematic multi-year changes in Eel River sediment

60

concentration led to a halving of 1965's maximum suspended-sediment concentration

approximately every decade -- and that these changes made rating curve calculations highly

sensitive to time dependencies of sediment concentrations. In Warrick (2014) he followed up on

this concern with further analysis, and found that Eel River sediment discharge rates were

overestimated by a factor of two in Wheatcroft and Borgeld (2000), as well as other stationary

rating curve calculations, including the HydroTrend calculations of Syvitski et al. (1998a). It is

thus virtually guaranteed that the HydroTrend-based calculations in this work suffer from a

similar large positive bias. Future work will need to incorporate nonstationary estimates, as

described in Warrick (2014).

Daily bedload is simulated depending on the delta plain slope S and the daily mean water

discharge Q[i] after the modified (Bagnold 1966) equation:

𝑄𝑏[𝑖] = 𝜌𝑠

𝜌𝑠− 𝜌 𝜌𝑔𝑄[𝑖]

𝛽𝑆𝑒𝑏

𝑔 tan𝜑 when 𝑢 ≥ 𝑢𝑐𝑟 (20)

where 𝜌𝑠 is sand density, 𝜌 is fluid density, eb is the bedload efficiency, 𝛽 is a dimensionless

bedload rating term, 𝜑 is the limiting angle of repose of sediment grains lying on the river bed, u

is stream velocity, and ucr is the critical velocity needed to initiate bedload transport.

Thus the total sediment load is calculated by adding the results of (19) and (20).

2.4.4 HydroTrend Eel Parameterization

Based on HydroTrend’s basin-wide Eel River parameters from earlier model implementations by

the creators (Syvitski et al. 1998), plus climatology statistics from the ERA-Interim atmospheric

forcing, the chosen parameters are listed in Table 2.1.

61

Table 2.1: Parameters used in HydroTrend calculations.

Symbol Meaning Value (and units)

Start Year 1979

Number of years run 64 (the first half is thrown away as spin-up,

the 1979-2010 climate repeats twice)

GWmax Maximum groundwater

storage

1.2e8 m3

GWmin Minimum groundwater storage 1.0e5 m3

GWstore Initial groundwater storage 5.0e5 m3

Pcr Critical rainfall rate for

minimal infiltration

10 mm/d

Pmax Rainfall rate to force

maximum hydraulic

conductivity

400.0 mm/d

K0 Saturated hydraulic

conductivity

374.0 mm/day

Moist adiabatic lapse rate to

calculate freezing line

8.9 ̊◦C/km

αgw Groundwater evaporation

coefficient

10 mm/d

βgw Groundwater exponent

coefficient

1 (unitless)

αss Groundwater subsurface storm

flow coefficient

700 m3/s

βss Groundwater subsurface storm

flow exponent coefficient

1.3 (unitless)

𝜔: BQART constant of

proportionality

0.02 kg/s/km/C

T Basin-averaged Temperature: 11.9 deg. C, standard deviation 0.54, derived

from ERA-Interim

A Total basin Area 8063 km2

L Lithology factor 2.0 (unitless)

Eh Anthropogenic factor 5.6 (unitless)

Te Reservoir trapping efficiency 0 (unitless)

Average river velocity 2.3 m/s

S Delta plane slope (rise-over-

run)

0.0007 m/m (unitless)

β Bedload rating term 1.0 (unitless)

eb Bedload efficiency 0.1 (unitless)

ucr Critical flow rate for bedload

transport

800 m3/s

Using these parameters in the equations above in sections 2.4.2 and 2.4.3, HydroTrend generates

time series of discharge Q, and sediment Qs + Qb. The subsequent circulation of that discharge is

62

modeled directly in the Regional Ocean Modeling System, described in section 2.5.11. Both

discharge and sediment are used to estimate Eel River nutrient loads in section 2.6.4.

In many respects HydroTrend is a pseudo-physics model; it has numerous fudge factors and

some broad assumptions (such as an arbitrarily imposed lag on groundwater discharge from

infiltration to export). Its inclusion in the modeling framework was an attempt to have riverine

output driven by the same atmosphere as the ocean model (since atmospheric forcing products

are themselves a product of some interpolation and estimation, with according uncertainties).

However, if this project was not an effort to use and connect models across land, atmosphere and

ocean, simply using USGS daily gauging data, and empirical estimates of sediment load such as

that which appears in Warrick et al. (2014), would certainly create a more realistic simulation.

63

2.5 Ocean Modeling: Regional Ocean Modeling System

2.5.1 Equations of Motion

As briefly described in section 2.2, the Regional Ocean Modeling System (Shchepetkin and

McWilliams 2005; Haidvogel et al. 2008; Arango 2014) solves the primitive equations on a

rotating Earth with finite difference approximations, advecting, diffusing and conserving

momentum, heat, salinity and (for our purposes) biological tracers of nitrate, phytoplankton,

zooplankton, and remineralizable detritus.

The primitive equations in Cartesian coordinates are reproduced here as expressed in Hedstrom

(2012). The momentum balance equations in the x- and y-directions are expressed as:

𝜕𝑢

𝜕𝑡+ 𝑣 ∙ ∇𝑢 − 𝑓𝑣 = −

𝜕∅

𝜕𝑥−𝜕

𝜕𝑧 𝑢′𝑤′ − 𝜈

𝜕𝑢

𝜕𝑧 + 𝐹𝑢 + 𝐷𝑢 (21)

𝜕𝑣

𝜕𝑡+ 𝑣 ∙ ∇𝑣 + 𝑓𝑢 = −

𝜕∅

𝜕𝑦−𝜕

𝜕𝑧 𝑣′𝑤′ − 𝜈

𝜕𝑣

𝜕𝑧 + 𝐹𝑣 + 𝐷𝑣

The time evolution of a scalar concentration field C(x,y,z,t) (e.g. salinity, temperature, or

nutrients), is governed by the advective-diffusive equation:

𝜕𝐶

𝜕𝑡+ 𝑣 ∙ ∇𝐶 = −

𝜕

𝜕𝑧 𝐶′𝑤′ − 𝜈𝜃

𝜕𝐶

𝜕𝑧 + 𝐹𝐶 + 𝐷𝐶 (22)

The equation of state is given by ρ = ρ(T,S,P), density as a function of temperature, salinity, and

total pressure. In the Boussinesq approximation, density variations are neglected in the

momentum equations except in their contribution to the buoyancy force in the vertical

momentum equation. Under the hydrostatic approximation, it is further assumed that the vertical

pressure gradient balances the buoyancy force:

𝜕∅

𝜕𝑧= −

𝜌𝑔

𝜌𝑜 (23)

The final equation expresses the continuity equation for an incompressible fluid:

𝜕𝑢

𝜕𝑥+

𝜕𝑣

𝜕𝑦+

𝜕𝑤

𝜕𝑧= 0 (24)

For the moment, the effects of forcing and horizontal dissipation will be represented by the

schematic terms F and D, respectively. These equations are closed by parameterizing the

Reynolds stresses and turbulent tracer fluxes as:

𝑢′𝑤′ = −𝐾𝑀𝜕𝑢

𝜕𝑧; 𝑣′𝑤′ = −𝐾𝑀

𝜕𝑣

𝜕𝑧; 𝐶′𝑤′ = −𝐾𝐶

𝜕𝐶

𝜕𝑧 (25)

64

An overbar represents a time average and a prime represents a fluctuation about the mean. The

variables used above (and at other points in this section) are shown in Table 2.2:

Table 2.2: Definitions of terms used in section 2.5.

Du, Dv, DC diffusive terms, with horizontal and vertical mixing schemes in ROMS

Fu, Fv, FC external forcing terms

f(y) Coriolis parameter

g acceleration of gravity

h(x,y) bottom depth

𝜈, 𝜈𝜃 molecular viscosity and diffusivity

Km, KC vertical eddy viscosity and diffusivity

P total pressure 𝑃 ≈ −𝜌𝑜𝑔𝑧

∅(𝑥,𝑦, 𝑧, 𝑡) dynamic pressure ∅ = (𝑃

𝜌𝑜)

𝜌𝑜 + 𝜌(𝑥,𝑦, 𝑧, 𝑡) total in situ density

S(x,y,z,t) salinity

t time

T(x,y,z,t) potential temperature

u,v,w the (x,y,z) components of vector velocity 𝑣 x,y horizontal coordinates

z vertical coordinate

𝜁(𝑥,𝑦, 𝑡) the surface elevation

𝜉(x,y) and η(x,y) curvilinear coordinate systems

𝑚(𝜉, 𝜂) and

𝑛(𝜉, 𝜂) scale factors relating the differential distances of the curvilinear coordinate

system to actual physical arc lengths

𝑆(𝑥,𝑦,𝜎) nonlinear vertical transformation functional

σ fractional vertical stretching coordinate

C(σ) monotonic, nondimensional vertical stretching function

hc critical depth for vertical stretching functions

𝜃𝑠 and 𝜃𝐵 surface and bottom control parameters for vertical stretching functions 𝐻𝑧𝑚𝑛

grid-box volume

𝐻𝑧𝛺

𝑚𝑛

finite-volume flux across the moving grid-box interface

𝛾 1/8, in ROMS

𝑖, 𝑗,𝑘 grid cell indices in the 𝜉, η and σ directions

N number of vertical levels (40)

QC surface concentration flux

𝜏𝑠𝑥 and 𝜏𝑠

𝑦 surface wind stress

𝜏𝑏𝑥 and 𝜏𝑏

𝑦 bottom stress

𝐶𝑝 specific heat of dry air

65

2.5.2 Curvilinear Coordinates

ROMS adopts a curvilinear grid in order to best resolve irregular boundaries and locally

increased grid resolution. Such a grid is created by introducing an appropriate orthogonal

coordinate transformation in the horizontal. Our new coordinates, 𝜉(x,y) and η(x,y), allow our

equations of motion to be re-written as per Arakawa and Lamb (1977), while leaving all of our

boundary conditions unchanged.

2.5.3 Vertical Coordinates

ROMS has a generalized terrain-following vertical coordinate system. There are two vertical

transformation equations available (Arango 2014) such that z = z(x,y,σ,t):

𝑧 = 𝑧(𝑥,𝑦,𝜎, 𝑡) = 𝑆(𝑥,𝑦,𝜎) + 𝜁(𝑥,𝑦, 𝑡) 1 +𝑆(𝑥,𝑦,𝜎)

ℎ(𝑥,𝑦) (26)

𝑆(𝑥,𝑦,𝜎) = ℎ𝑐𝜎 + [ℎ(𝑥,𝑦) − ℎ𝑐]𝐶(𝜎) (Transformation 1)

or:

𝑧(𝑥, 𝑦,𝜎, 𝑡) = 𝜁(𝑥,𝑦, 𝑡) + [𝜁(𝑥,𝑦, 𝑡) + ℎ(𝑥,𝑦)]𝑆(𝑥,𝑦,𝜎) (27)

𝑆(𝑥,𝑦,𝜎) = ℎ𝑐𝜎 + ℎ(𝑥, 𝑦)𝐶(𝜎)

ℎ𝑐 + ℎ(𝑥,𝑦)

(Transformation 2)

where 𝑆(𝑥,𝑦,𝜎) is a nonlinear vertical transformation functional, 𝜁(𝑥,𝑦, 𝑡) is the time-varying

free-surface, ℎ(𝑥,𝑦) is the unperturbed water column thickness and z = -h(x,y) corresponds to

the ocean bottom, σ is a fractional vertical stretching coordinate ranging from −1 ≤ 𝜎 ≤ 0, C(σ)

is a nondimensional, monotonic, vertical stretching function ranging from −1 ≤ 𝐶(𝜎) ≤ 0, and

hc is a positive thickness controlling the stretching.

Although Transformation 2 is widely considered the superior choice, because it recovers the true

sigma-coordinate system as ℎ𝑐 → ∞, provides equally-spaced sigma coordinates in shallow

regions, and reduces pressure gradient errors (Schchpetkin and McWilliams 2005), it was found

in this project to be the source of unconditional instability. Blow-ups both at the northwest and

southeast boundary corners, as well as over the complex bathymetry of the Mendocino Triple

Junction, were not present when using transformation 1 instead. However, transformation 2 was

used successfully at 10 km resolution. This is one of many differences between the 10 and 1 km

models, summarized in section 2.7.

There are also four vertical stretching functions available (Arango 2014), 𝐶(𝜎). This is a

dimensionless, nonlinear, monotonic, continuous differentiable (or at least differentiable

66

piecewise with smooth transition) function, that must be discretized at fractional stretched

vertical coordinate 𝜎,

𝜎(𝑘) =

𝑘−𝑁

𝑁,𝑎𝑡 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝑊 𝑝𝑜𝑖𝑛𝑡𝑠,𝑘 = 0,… ,𝑁

𝑘−𝑁−0.5

𝑁,𝑎𝑡 𝑣𝑒𝑟𝑡𝑖𝑐𝑎𝑙 𝜌 𝑝𝑜𝑖𝑛𝑡𝑠,𝑘 = 1,… ,𝑁

(28)

Finally, 𝐶(𝜎) must be constrained by −1 ≤ 𝐶(𝜎) ≤ 0, that is,

𝐶(𝜎) = 0,𝑓𝑜𝑟 𝜎 = 0,𝑎𝑡 𝑡ℎ𝑒 𝑓𝑟𝑒𝑒 − 𝑠𝑢𝑟𝑓𝑎𝑐𝑒;−1,𝑓𝑜𝑟 𝜎 = −1,𝑎𝑡 𝑡ℎ𝑒 𝑜𝑐𝑒𝑎𝑛 𝑏𝑜𝑡𝑡𝑜𝑚.

(29)

The original stretching function, Vstretching = 1, from (Song and Haidvogel 1994) behaved best

for our 1 km model (though we used Vstretching = 4 for the 10 km resolution application):

𝑉𝑠𝑡𝑟𝑒𝑡𝑐ℎ𝑖𝑛𝑔 = 1 → 𝐶(𝜎) =(1−𝜃𝐵)sinh(𝜃𝑠𝜎)

sinh(𝜃𝑠)+ 𝜃𝐵

tanh[𝜃𝑠 𝜎+1

2 ]

2tanh(1

2𝜃𝑠)

−1

2 (30)

where 𝜃𝑠 and 𝜃𝐵 are the surface and bottom control parameters. Their ranges are 0 < 𝜃𝑠 ≤ 20

and 0 < 𝜃𝐵 ≤ 1, respectively. For our application, 𝜃𝑠 = 5, and 𝜃𝐵 = 0.3.

2.5.4 Domain and Grid Spatial Resolution

Due to the nature of curvilinear coordinates, the model’s grid cells have some variation in size.

To achieve an average horizontal grid size of 1 km, and to keep the open boundaries sufficiently

far from the region of interest in order to minimize the effect of inevitable boundary difficulties,

ROMS was configured to range from 39.0036 to 42.1966 N, -123.507 to 128.993 W, with 374 x

453 interior horizontal points. The 10 km grid ranged from 37-47 N, -132-123 W, with 275 x

556 interior horizontal points. ROMS only performs ocean circulation calculations; thus, land

was masked off using the NOAA Medium Resolution Shoreline (NOAA 2012b), which has an

average scale of 1:70,000. All grid cells beneath the land mask are not part of the calculations;

the ocean-coastline boundary is a simple closed wall, disallowing water transport further inland.

No atmosphere-land interactions or river modeling, is performed beneath the land mask;

generation of riverine boundary conditions is performed by HydroTrend (section 2.4) and

implemented as described in section 2.5.11. The grid was created with the SeaGrid grid

generation MATLAB package (Signell 2013).

67

Figure 2.17: The spatial extent of the two ROMS domains.

The vertical structure of the grid consists of terrain following levels, discussed in section 2.5.3.

However, beyond curvilineal coordinates and stretching functions, s-levels are also defined such

that:

𝑆(𝑥,𝑦,𝜎) = 0, 𝑖𝑓 𝜎 = 0,𝐶(𝜎) = 0,𝑎𝑡 𝑡ℎ𝑒 𝑓𝑟𝑒𝑒 − 𝑠𝑢𝑟𝑓𝑎𝑐𝑒;

−1, 𝑖𝑓 𝜎 = −1,𝐶(𝜎) = −1,𝑎𝑡 𝑡ℎ𝑒 𝑜𝑐𝑒𝑎𝑛 𝑏𝑜𝑡𝑡𝑜𝑚; (31)

The use of s-levels allows all measurements at the s-level closest to the surface to happen at

roughly the same depth, regardless of the bathymetry of the area. The “true” sigma-coorinate

system is recovered as hc approaches infinity. This application of ROMS uses 40 vertical levels.

Our choice of stretching parameters puts the majority of the vertical resolution at the surface,

where the plume will be resolved, while having enough resolution at the bottom to not create

undue numerical instability, and to resolve Ekman transport and upwelling dynamics as

realistically as possible.

68

Figure 2.18: A graphical representation of the terrain-following vertical structure of the grid,

taken across a vertical transect from eastern to western boundary at a latitude of 40 N. The x-

axis is longitude. Note that the long flat stretch to the west is land, and masked off from the

simulation.

2.5.5 Bathymetry

The bathymetry in our grid was initially extracted from the STRM30_PLUS V8.0 dataset, a

global 30 arcsecond grid (Becker et al. 2009). To reduce poor behavior over sharp slopes, it was

considerably smoothed using second and fourth-order Shapiro filters (Shapiro 1970) until all

adjacent grid cells had an r-factor (ℎ1−ℎ2)

(ℎ1+ℎ2) less than 0.35. The Shapiro filter is a high order

horizontal filter that efficiently removes small grid scale noise without affecting the physical

structures of a field. Despite this smoothing, care was taken to preserve the important local

features, including the offshore Eel Canyon where most Eel sediment has historically been found

to deposit (Mullenbach et al. 2004) and the Mendocino Scarp, a 1500m interface between two

tectonic plates, the Pacific Plate and the Juan de Fuca Plate. Along with the North American

Plate, these plates create the Mendocino Triple Junction: a geologic triple junction where the San

Andreas Fault meets the Mendocino Fault and the Cascadia subduction zone. While the

geologic-timescale dynamics are not of interest to us, this is a bathymetrically complex region of

the ocean floor, and creates considerable difficulties in ROMS with false pressure gradients and

69

unstable deep water masses. It is the obvious culprit for an important model artifact (see Chapter

3.8), but this is preferable to smoothing it completely away and losing all the physical dynamics

its presence imposes on local ocean circulation.

2.5.6 Temporal Resolution and Numerics

ROMS uses a split timestep, resolving barotropic and baroclinic equations separately (Haidvogel

et al. 2008). Although many ROMS applications on the mesoscale can run on timesteps of five

or ten minutes or more, the 1 km model runs on a 30 second baroclinic timestep, and a 1 second

barotropic timestep. This was necessary not because of the horizontal resolution but because of

the implementation of the river; the salinity gradients created by freshwater entering the ocean

are numerically unstable, quick to become negative, or explode to unreasonably high values.

Using 𝑚(𝜉, 𝜂) and 𝑛(𝜉, 𝜂) as the scale factors which relate the differential distances (Δη,Δξ) to

the actual (physical) arc lengths, the advection of a tracer C has an equation (Arango 2014) of the

form

𝜕

𝜕𝑡

𝐻𝑧𝐶

𝑚𝑛= −

𝜕

𝜕𝜉𝐹𝜉 −

𝜕

𝜕𝜂𝐹𝜂 −

𝜕

𝜕𝜎𝐹𝜎 (32)

where we have introduced the advective fluxes:

𝐹𝜉 =𝐻𝑧𝑢𝐶

𝑛; 𝐹𝜂 =

𝐻𝑧𝑣𝐶

𝑚; 𝐹𝜎 =

𝐻𝑧𝛺𝐶

𝑚𝑛 (33)

Horizontal momentum was discretized with a third-order upstream bias advection scheme with

velocity dependent hyper-viscosity. The two-dimensional scheme in ROMS is called UTOPIA

(Uniformly Third-Order Polynomial Interpolation Algorithm: Rasch 1994, Shchpetkin and

McWilliams 1998). UTOPIA can be used on variables with both positive and negative values,

making it suitable for momentum calculations as well as scalars such as temperature and salinity.

For the u-velocity, we have:

𝐹𝜉 = 𝑢 − 𝛾𝜕2𝑢

𝜕𝜉2 [

𝐻𝑧𝑢

𝑛− 𝛾

𝜕2

𝜕𝜉2 𝐻𝑧𝑢

𝑛 ]

𝐹𝜂 = 𝑢 − 𝛾𝜕2𝑢

𝜕𝜂2 [

𝐻𝑧𝑣

𝑚− 𝛾

𝜕2

𝜕𝜉2 𝐻𝑧𝑣

𝑚 ] (34)

𝐹𝜎 =𝐻𝑧𝑤

𝑚𝑛[−

1

16𝑢𝑖,𝑗,𝑘−1 +

9

16𝑢𝑖,𝑗,𝑘 +

9

16𝑢𝑖,𝑗,𝑘+1 −

1

16𝑢𝑖,𝑗,𝑘+2]

while for the v-velocity we have:

𝐹𝜉 = 𝑣 − 𝛾𝜕2𝑣

𝜕𝜉2 [

𝐻𝑧𝑢

𝑛− 𝛾

𝜕2

𝜕𝜉2 𝐻𝑧𝑢

𝑛 ]

𝐹𝜂 = 𝑣 − 𝛾𝜕2𝑣

𝜕𝜂2 [

𝐻𝑧𝑣

𝑚− 𝛾

𝜕2

𝜕𝜉2 𝐻𝑧𝑣

𝑚 ] (35)

𝐹𝜎 =𝐻𝑧𝑤

𝑚𝑛[−

1

16𝑣𝑖,𝑗,𝑘−1 +

9

16𝑣𝑖,𝑗,𝑘 +

9

16𝑣𝑖,𝑗,𝑘+1 −

1

16𝑣𝑖,𝑗,𝑘+2]

70

In all these terms, the second derivatives are evaluated at an upstream location.

Vertical momentum was discretized with a fourth-order, centered differences scheme:

𝐹𝑠 =𝐻𝑧𝑤

𝑚𝑛[−

1

16𝐶𝑖,𝑗,𝑘−1 +

9

16𝐶𝑖,𝑗,𝑘 +

9

16𝐶𝑖,𝑗,𝑘+1 −

1

16𝐶𝑖,𝑗,𝑘+2] (36)

There is some implicit viscosity associated with this discretization, as the numerical error is

diffusive in nature, though not as serious as it would be with a first or second-order upwinding

scheme (Haidvogel et al. 2008). This error, however, helps to counteract the tendency of the

model to destroy its own onshore water column stratification, which is functionally spurious

numerical upwelling. (For more on model viscosity, see section 2.5.7.)

Although the model could resolve temperature, salinity, and the biological tracers

(phytoplankton, zooplankton, NO3 and detritus) using UTOPIA, this configuration uses what is

called recursive MPDATA (Multidimensional Positive Definite Advection Transport Algorithm,

Smolarkiewicz 1984, 1986, 1990) three-dimensional advection instead. MPDATA provides a

hard clamp on the positivity of tracer values; it is monotonic and maintains the extrema. Without

it, salinity and zooplankton, in particular, have a tendency to go unphysically negative. It is

marginally more computationally expensive, but ultimately worth the price. An example of

MPDATA’s discretization scheme is found in (Tsujino 2010).

2.5.7 Horizontal Diffusion and Viscosity

The model uses linear bottom friction of momentum, but second-order diffusion for the tracers (8

m2/s, a standard value seen in common use [Arango 2014]), and second-order viscosity for

momentum. In ROMS, the viscosity is derived from the horizontal divergence of the deviatory

stress tensor (Wajsowicz 1993); in our specific application we use viscosity to reduce spurious

numerical upwelling by simply making the water resist motion a little more, and so its value is

increased to 20 m2/s. This is still well within values found in the literature, which in large-scale

applications can range as high as 1000 m2/s (Jochum et al. 2008). The mixing of momentum and

tracers is applied along geopotential (constant depth) levels.

2.5.8 Vertical Mixing Parameterization

K-profile vertical parameterization (Large et al. 1994) of the viscous and diffusive coefficients is

perhaps the most widely used ocean mixing schemes in ROMS and certainly the default (Arango

2014). Although it was usable for our 10 km model (see section 2.7), it was an arduous process

to pick apart the scope of its inability to resolve pressure gradients for the 1 km application.

Eventually it was replaced with the Mellor-Yamada 2.5 closure scheme (Mellor and Yamada

1982), modified as described in Galperin et al. 1988 and Allen et al. 1995.

71

2.5.9 Boundary Conditions

2.5.9.1 Lateral Boundary Conditions

By dint of being along the west coast of the United States, the domain (see Figure 2.17) has three

open lateral boundary conditions, to the west, north, and south. (The east is simply a closed wall

boundary for the coastline.) Doing a good job with open boundaries has been a major challenge

of ocean circulation modeling for decades, a challenge that persists now (Marchesiello et al.

2001). One mitigating solution is to place the boundaries much further from the region of

interest in the model than they might otherwise be, moving the modeling artifacts safely away at

the expense of computational cost. That was done here, as there is no need to simulate all the

way up to Washington State to resolve questions about the Eel River’s impact on coastal ocean

primary productivity. The southern boundary is considerably closer to Cape Mendocino, but

avoids having to deal with San Francisco Bay, which seemed to have larger impacts than a more

distant boundary. The major model artifact (Chapter 3.8) is due to the southeastern corner of the

model poorly advecting momentum that has come off the Mendocino Triple Junction, interacting

with southern boundary instability.

Lateral boundary conditions must be specified for the free-surface, 2D and 3D horizontal

velocity, mixing turbulent kinetic energy, temperature, salinity, and biological tracers. For a

summary of the boundary conditions used, see Table 2.3:

Table 2.3: Lateral boundary conditions used for the ocean circulation model.

Free-surface Chapman Boundary Conditions

2D UV Momentum Flather Boundary Conditions

3D UV Momentum Radiation+Nudging with sponge layer

Temperature Radiation+Nudging with sponge layer

Salinity Radiation+Nudging with sponge layer

Phytoplankton, Zooplankton Radiation+Nudging

NO3, Detritus Radiation+Nudging

Flather Boundary Conditions: In Flather 1976, it was proposed to radiate out deviations of

barotropic velocity from exterior values at the speed of external gravity waves:

𝑢 = 𝑢 𝑒𝑥𝑡 − 𝑔

𝐷(𝜁 − 𝜁𝑒𝑥𝑡) (37)

Chapman Boundary Conditions: The equivalent of Flather for surface elevation was invented

by Chapman (1985); it assumes all outgoing signals leave at the shallow-water wave

approximation speed of 𝑔𝐸, where E is depth. Then, the rate of change of the free elevation in

time is simple the gradient of the free elevation in space times the speed, solved implicitly rather

than explicitly in ROMS:

𝜕𝜁

𝜕𝑡= ± 𝑔𝐸

𝜕𝜁

𝜕𝜉 (38)

72

Radiation-Nudging Boundary Conditions: In order to properly resolve simultaneous inflow

and outflow along the same boundary, sometimes even at different depths at the same horizontal

location, a radiation boundary condition was formulated (Orlanski 1976) that uses a local normal

phase velocity to radiate things out; in Raymond and Kuo 1984 the issue of transport

approaching the boundary at an angle was improved.

𝜕∅

𝜕𝑡= − ∅𝜉

𝜕∅

𝜕𝜉+ ∅𝜂

𝜕∅

𝜕𝜂 (39)

where

∅𝜉 =𝐹𝜕∅

𝜕𝜉

𝜕∅

𝜕𝜉 2+

𝜕∅

𝜕𝜂 2

∅𝜂 =𝐹𝜕∅

𝜕𝜂

𝜕∅

𝜕𝜉 2+

𝜕∅

𝜕𝜂 2 (40)

𝐹 = −𝜕∅

𝜕𝑡

To handle inflow, nudging to a known exterior value is performed per Marchesiello et al. (2001);

physical exterior values were provided by NASA’s ECCO2 dataset (Menemelis et al. 2008) for

the 10 km model, and by 10 km results for the 1 km model. Biological exterior values came

from the World Ocean Database (NOAA 2013b) and World Ocean Atlas (NOAA 2013c; see

section 2.6.3 for both WOD and WOA descriptions), for phytoplankton and nitrogen

respectively; zooplankton were assumed to be 10% of phytoplankton, while detritus was set to a

constant value of 0.001 mmol/m3. In both cases, monthly climatologies were calculated and

used for the boundary conditions. Inflow nudging is applied once per day, while outflow

nudging is applied once per four months (since the majority of outflow is handled by the

radiation condition).

Furthermore, nudging is applied over a sponge layer, which is to say, the ten outermost points of

the grid are all nudged with a strength of (100-10*distance from the boundary), such that the

boundary point experiences the full, 100% strength of nudging, while the point ten inwards

experiences 10% of that effect. This improves the numerical stability of the boundary by

preventing large gradients from forming over only a couple of grid cells.

2.5.9.2 Bottom boundary conditions

The horizontal velocity has linear bottom friction applied as a bottom stress. Because tracers

cannot move below the ocean floor, their concentration flux is set to zero. Hedstrom (2012)

summarizes their prescription as follows:

73

Top boundary 𝑧 = 𝜁(𝑥,𝑦, 𝑡) :

𝐾𝑚𝜕𝑢

𝜕𝑧= 𝜏𝑠

𝑥(𝑥,𝑦, 𝑡)

𝐾𝑚𝜕𝑣

𝜕𝑧= 𝜏𝑠

𝑦(𝑥, 𝑦, 𝑡) (41)

𝐾𝐶𝜕𝐶

𝜕𝑧=

𝑄𝐶𝜌𝑜𝐶𝑝

𝑤 =𝜕𝜁

𝜕𝑡

Bottom boundary (𝑧 = −ℎ(𝑥,𝑦)):

𝐾𝑚𝜕𝑢

𝜕𝑧= 𝜏𝑏

𝑥(𝑥,𝑦, 𝑡)

𝐾𝑚𝜕𝑣

𝜕𝑧= 𝜏𝑏

𝑦(𝑥,𝑦, 𝑡) (42)

𝐾𝐶𝜕𝐶

𝜕𝑧= 0

−𝑤 + 𝑣 ∙ ∇ℎ = 0

where QC is the surface concentration flux, 𝜏𝑠𝑥 and 𝜏𝑠

𝑦 comprise the surface wind stress, and 𝜏𝑏

𝑥

and 𝜏𝑏𝑦

the bottom stress.

2.5.10 Surface Model Forcing

The surface boundary conditions are controlled by the atmosphere; winds impose surface stress

of momentum, while heat radiates in and out. We have reviewed the spatial and temporal

resolution of the atmospheric forcing datasets used in section 2.3. To apply them in ROMS, they

are first interpolated onto the horizontal grid; at each timestep, ROMS takes a weighted average

of the two nearest forcing time points, and applies the result. While in the 10 km model, bulk

flux approximations (Tsujino 2010 has an excellent summary, not reproduced here) were used to

estimate surface stress from wind speed, the breakdown of the Monin-Obukov equations when

assumptions of atmospheric stability are no longer true, caused them to behave poorly (see

Section 2.3.2). For the 1 km model, surface stress provided directly from the ERA Interim

analysis was used instead, reducing model error. Additionally, ERA surface freshwater flux

(evaporation minus precipitation), net surface radiation, and net surface heat flux were applied.

Monthly climatologies of sea surface temperature and sea surface salinity from the same analysis

were used to correct the net heat flux and freshwater flux, nudging them on a daily timescale

much like the lateral boundary conditions described in Section 2.5.9.1, with the commonly used

surface net heat flux sensitivity to sea surface temperature dQnet/dSST of -40 W/m2/Celsius.

Atmospheric deposition of nitrogen was not considered in this model as previous studies have

found it to be of relatively little importance in this region (Krishnamurthy et al. 2009, Okin et al.

2011), and surface forcing of phytoplankton, zooplankton and detritus were all zero as well.

74

Table 2.4: Atmospheric forcing fields and their units, as applied directly to the sea surface with

the ERA-Interim dataset.

Forcing Field Units

surface U-momentum stress Pa (N/m2)

surface V-momentum stress Pa (N/m2)

net shortwave radiation flux Watts/m2

net longwave radiation flux Watts/m2

net sensible heat flux Watts/m2

sea surface salinity PSU

sea surface temperature Celsius

surface net heat flux sensitivity to SST Watts/m2/Celsius

net surface heat flux Watts/m2

net surface freshwater flux cm/day

2.5.11 River Forcing

The river was applied as a lateral boundary condition. In order to resolve advection properly, the

river channel cut into the land mask was a bare minimum of three grid cells wide – at 1 km

resolution this makes for an excessively wide Eel River, but it was an unavoidable compromise,

as the model could not support variable widths or depths, nor increased horizontal resolution due

to the computational expense. In effect, this modeling framework perpetually assumes an Eel

River in extreme flood conditions, because that is the time that the river is most likely to have

immediate short-term impacts on coastal primary productivity as it delivers its large nutrient

load. Naturally this introduces a loss of realism. The mouth of the Eel River includes a 30m

wide channel that widens to 400m by the time it crosses the sand flats and reaches the ocean

(Schlosser and Eicher 2012). During major storm events the Eel River often floods (and thus

widens) considerably, as captured by satellite and aircraft imagery (Leithold 1974, NASA 2012),

but 3 km is still typically an order of magnitude too wide.

However, images like these also capture the large physical scales of offshore transport; sediment

and nutrients are caught up by ocean circulation and advected by 10 km, 25 km, or more, and a 1

km horizontal resolution can simulate many of the eddies and currents in play. The ability of a 1

km horizontal resolution, 3 km wide Eel River channel numerical simulation to capture physical

properties of the plume has been tested for the January 1997 floods (Pullen and Allen 2000,

Pullen and Allen 2001), and modeling at this scale was generally successful at reproducing

measurements of plume extent, depth and velocity.

Since the Eel River is not always flooding, however, this channel width creates vastly lower

input velocities (in order to distribute the water-per-time across such an input volume), and even

at high levels of discharge these lower velocities could not carry bedload. This is the major

reason why the model does not attempt to simulate sediment transport directly; instead (as

described in section 2.6.4) it simulates dissolved and particulate nitrogen.

75

Additionally, applying the river across these three cells right at the mouth creates enormous

salinity gradients that become numerically unstable very quickly; therefore the river ‘begins’

three grid cells back, at the end of a short channel. Out of concern for possible lags in plume

delivery, this distance was determined across multiple short experiments to be the best

compromise between a softer initial salinity gradient and time lag for the river to travel down the

channel – its lag is negligible, though the gradient is large enough to necessitate extremely short

timesteps to maintain numerical stability.

As noted in section 2.4, HydroTrend results provide a daily time series of freshwater discharge

and sediment mass. The water is distributed into the forty vertical levels of the 10 m deep

channel, and split across the three cells such that the initial velocity in the central cell is 50%

greater than that of the sides, which should be experiencing drag. The water temperature profile

is constant throughout the column to represent the extreme turbulence of storm conditions (and

while this is certainly wrong much of the year, those are precisely those times of year that the

river is very small). Temperature is dictated by a monthly climatology calculated from USGS

data (USGS 2012) gauged at Scotia, CA, 23 miles north of the mouth. Satellite and aircraft

imagery (Leithold 1974, NASA 2012) as well as during-storm cruises of STRATAFORM

(Wheatcroft et al. 1997) make it clear that the Eel plume is often advected on the surface of the

ocean rather than experiencing hyperpycnal flow (eg, so dense with sediment that it flows along

the bottom of the shelf, rather than the surface); however, the colder water in January and

February from the Scotia climatology was sinking as compared to the ROMS ocean purely due

to temperature effects on density. This seemed unrealistic, so allowing for the possibility that the

river is warming between Scotia and the mouth, the values for January and February were

increased to a minimum of 9 ̊ Celsius for this effect to not dominate the flow in the model.

For the description of the biological aspects of the river in ROMS, see section 2.6.4.

2.5.12 Model Initialization and Spinup

The model must be initialized with values of momentum, temperature, salinity, and pressure at

every point on the grid. Although the 10 km ROMS results could easily provide initial values for

the 1 km version, initializing with ECCO2 (Menemenlis 2008) created more consistent

numerical stability. This sensitivity to initialization is due to the model’s tendency to have large

motions of water masses as the stratification works itself out; the pressure gradient errors are at

their maximum within the first few time steps, and indeed it takes many time steps to spin up

sufficiently such that results can be collected.

Conversely, running a model like ROMS for too long causes cumulatively accumulating errors

of spurious diapycnal diffusion to eventually cause unstable water masses and a total breakdown

of onshore stratification. This is a known issue in the modeling community, and an active area

of research in advection schemes that combat the issue (Marchesiello et al. 2009, Lamrie et al.

2012), but no ROMS-Rutgers schemes were found to be useful. The 10 km results, which were

generated by a continuous run from 1998-2010, begin to suffer from this starting around 2008,

though they are still suitable for boundary conditions as the boundaries are by definition almost

entirely far from shore. The 1 km model’s results become notably infected with this error after

76

about eighteen months, so a continuous decadal run at this higher resolution was out of the

question.

Thus eighteen months of continuous modeling was available to be distributed between spin-up

and results collection. A collection period of a full year was desired in order to have within-year

internal consistency on the various nonlinear footprints of numerical error (which vary from

year-to-year because of the variable atmospheric forcing), which left a maximum of six months

for spinup. Common practice in ROMS is to spin up for more like three months (Arango 2014);

however, this conventional wisdom did not prove out in the 1 km application. Even at six

months there were still vestiges of an initial model artifact, momentum being falsely reflected

around the southwestern corner; this artifact is discussed in further depth in section 3.9. In

hindsight, it would be worthwhile to spin up for 8 months and collect for 10; it is not even

particularly necessary to calculate results for September and October, since the river is at its

minimum during that period. Unfortunately the computational expense and sheer amount of

model runtime made such a re-run prohibitive for this thesis.

Each year of continuously collected data runs from November through the following October

(since Eel storm events between 1998-2010 occur no earlier than November). Thus the model

initializes on May 1, works out the worst of its instabilities over the summer, and is ready to

manage the storm events come autumn, when the Eel River begins delivering its nutrient loads.

2.6 Biogeochemical Modeling: Nutrient-Phytoplankton-Zooplankton-Detritus

2.6.1 NPZD description and limitations

The coupled modeling framework uses the NPZD ([total] Nitrogen-Phytoplankton-Zooplankton-

Detritus) model coupled into the Regional Ocean Modeling System from Powell et al. (2006). In

the same paper, a literature review of modeling efforts leading up to that point is described.

Since 2006, Powell-NPZD has been used in many applications, including expansions such as

iron limitation (Fiechter et al. 2009), superior parameter estimation using surrogate-based

optimization (Priess et al. 2013) and Bayesian hierarchical modeling (Fiechter et al. 2013; Milliff

et al. 2013). A thorough analytical analysis of NPZD’s internal dynamics identifies three

equilibria, one where there are available nutrients but no organisms taking them up; and two

where nutrients, phytoplankton and detritus exist in a balanced state (Heinle and Slawig 2013).

Absent from Powell-NPZD is a distinction between forms of nitrogen, multiple size (or other

distinct) classes of phytoplankton or zooplankton, and any effects from higher trophic levels.

As described in Powell et al. (2006) and visualized in Figure 2.19, Powell-NPZD is a four-

element, nitrogen-based trophic model, in which nitrogen is partitioned between the dissolved

(N) and particulate (D) phases, as well as between phototrophic phytoplankton (P) and

herbivorous zooplankton (Z). In the model, local time derivatives and an advective term are

balanced by vertical mixing, and a given element’s growth and mortality.

𝜕𝑁

𝜕𝑡+ 𝒖 ∙ ∇𝑁 = 𝛿𝐷 + 𝛾𝑛𝐺𝑍 − 𝑈𝑃 +

𝜕

𝜕𝑧 𝑘𝜈

𝜕𝑁

𝜕𝑧 (43)

77

𝜕𝑃

𝜕𝑡+ 𝒖 ∙ ∇𝑃 = 𝑈𝑃 − 𝐺𝑍 − 𝜎𝑑𝑃 +

𝜕

𝜕𝑧 𝑘𝜈

𝜕𝑃

𝜕𝑧 (44)

𝜕𝑍

𝜕𝑡+ 𝒖 ∙ ∇𝑍 = (1 − 𝛾𝑛)𝐺𝑍 − 𝜁𝑑𝑍 +

𝜕

𝜕𝑧 𝑘𝜈

𝜕𝑍

𝜕𝑧 (45)

𝜕𝐷

𝜕𝑡+ 𝒖 ∙ ∇𝐷 = 𝜎𝑑𝑃 + 𝜁𝑑𝑍 − 𝛿𝐷 +𝑤𝑑

𝜕𝐷

𝜕𝑧+

𝜕

𝜕𝑧 𝑘𝜈

𝜕𝐷

𝜕𝑧 (46)

𝐺 = 𝑅𝑚(1 − 𝑒−𝛬𝑃) (47)

𝐼 = 𝐼0exp 𝑘𝑧𝑧 + 𝑘𝑝 𝑃(𝑧′)𝑑𝑧′𝑧

0 (48)

𝑈 =𝑉𝑚𝑁

𝑘𝑁+𝑁

𝛼𝐼

𝑉𝑚2+𝛼2𝐼2

(49)

U represents the photosynthetic growth and uptake of nitrogen by phytoplankton; G represents

grazing on phytoplankton by zooplankton, mortality is represented with 𝜎𝑑 for phytoplankton

and 𝜁𝑑 for zooplankton, and sinking and remineralization of detritus (wd and 𝛿 respectively).

Light at depth z assumes exponential attenuation by seawater (kz) and phytoplankton (kp). A

Michaelis-Menten curve is used to describe the change in phytoplankton uptake rate as a

function of nitrogen concentration, while zooplankton grazing uses the Ivlev function, including

the possibility of “sloppy feeding” causing some nitrogen to go directly to detritus instead of the

zooplankton element. Mortality and remineralization are linear functions of concentration,

allowing dead plankton to become detritus, and detritus to be remineralized to dissolved

nitrogen.

78

Figure 2.19 (from Banas 2009b): The structure of an NPZD-type ecosystem model.

The parameters provided by Powell et al. (2006) are well-tested in both the California current

and off of Oregon, making them suitable for use in northern California.

Table 2.5: Powell et al. (2006) parameters used for Powell-NPZD.

Parameter name Symbol Value Dimension

Light extinction coefficient kz 0.067 m-1

Self-shading coefficient kp 0.0095 m2

mmol-N-1

Initial slope of P-I curve α 0.025 m2 W

-1

Surface irradiance IO 158.075 W m-2

Nitrate uptake rate Vm 1.5 d-1

Uptake half saturation kN 1.0 mmol-N m-3

Phytoplankton senescence 𝜎𝑑 0.1 d-1

Zooplankton grazing rate Rm 0.52 d-1

Ivlev constant Λ 0.06 m3

mmol-N-1

Excretion efficiency 𝛾𝑛 0.3

Zooplankton mortality 𝜁𝑑 0.145 d-1

Remineralization 𝛿 1.03 d-1

Detrital sinking rate wd 8.0 m d-1

79

2.6.2 NPZD ROMS dynamics

Nitrogen, Phytoplankton, Zooplankton and Detritus are advected and diffused with the

temperature and salinity fields. Unlike in Powell et al. (2006), positive definite behavior is

proscribed with use of the MPDATA advection scheme (see section 2.5.6). This was

necessitated by both the nitrogen and zooplankton terms going negative despite the application

of a conservative filter. In choosing MPDATA, the conservative filter could be removed.

Lateral harmonic horizontal diffusion constants were set to 4 m2/s. Radiation-Nudging lateral

boundary conditions were applied to Powell-NPZD terms, as described in section 2.5.9.1.

2.6.3 NPZD initial and boundary conditions

The World Ocean Database (NOAA 2013b) has an array of cruise-sampled phytoplankton

concentration data, which can be interpolated geographically and temporally to create a set of

monthly averages to be applied each year. This data was used for both initial and boundary

conditions of phytoplankton, with zooplankton and detritus initialized to 10% of the

phytoplankton value. It is, however, in units of micrograms of chlorophyll-a (chla) per litre of

water. As Powell-NPZD is a nitrogen-based model, a unit conversion is necessary:

μg chla

L

μg C

μg chla

μmol C

μg C

μmol N

μmol C=

μmol N

L (50)

The Redfield Ratio of atomic mass in phytoplankton (C:N:P = 106:16:1; Redfield 1934) is

applicable, but the key uncertainty here is in the chl-a/Carbon ratio, which varies widely based

on environmental conditions and phytoplankton speciation. It is not constant, changing under

the effects of light, nutrients, and temperature. 50 C:Chl is a reasonable compromise taken from

a study of this ratio in the California current (Li et al. 2010); for more discussion of the model

uncertainty introduced by this unknown parameter, see section 3.8.

The World Ocean Atlas (NOAA 2013c) is a set of objectively analyzed (1̊ grid) climatological

fields, including in situ nitrate, which was used to create both initial and boundary conditions for

nitrogen. As for the physical fields, all initial and boundary condition interpolation was

performed in MATLAB.

2.6.4 NPZD riverine input

Riverine dissolved inorganic nitrogen (ammonia, ammonium, and nitrate, though in the Powell-

NPZD model there is only one “nitrate” variable for all of these) was calculated from USGS data

(USGS 2012) and found to be, on average, constant throughout the year (Figures 2.20 and 2.21).

The USGS total nitrogen data in Figures 2.20 and 2.21 was collected between 1954-1998 at

Scotia, surely using a variety of sampling and analysis methods over the 40 year period. Based

on Fishman et al. 1994, which lists all USGS organic and inorganic analysis methods and the

years in which they were used by the agency, it is most likely that total nitrogen as nitrate plus

nitrite was most often measured using colorimetry analysis, typically with a cadmium reduction-

diazotization, as described in Fishman and Friedman 1989 and Fishman 1993. A measurement

80

of total nitrogen by digestion-distillation titrimetry was also widely used from 1978-1988

(Fishman and Friedman 1989) which is when many of these measurements were taken.

Figure 2.20: Figure by Dr. Jonah Piovia-Scott. USGS nutrient concentrations at Scotia, CA

taken between 1959-present, and monthly climatological averages.

81

Figure 2.21: Figure by Dr. Jonah Piovia-Scott. USGS nutrient flux at Scotia, CA calculated by

multiplying nutrient concentration at time of measurement by measured river discharge at time

of measurement, and monthly climatological averages. The flux is clearly dominated by the

increased river discharge in the winter.

Figures 2.20 and 2.21 indicate that during storm events there is a larger flux of nitrogen due to

more water discharged, but the nitrogen concentration within that water seems to remain the

same. It is possible that very short-term effects of leaching could be detected with a high-

frequency data sampling, and the model climatology updated accordingly, but that is beyond the

scope of this thesis.

The possibility of the river delivering living microorganisms who would then prosper in the

ocean (phytoplankton and zooplankton) was not tested in the model, but river detritus was

considered seriously as a possible source of local, short-timescale pulses of phytoplankton

productivity, as they uptake what is available to them in the freshly delivered organic matter of

Cape Mendocino; additionally, due to the remineralization rate allowed for in the biological

model, river “detritus” could include slowly bioavailable nutrients in the sediments themselves.

82

Therefore, HydroTrend’s estimate of sediment mass transport of the river was used, in turn, to

estimate time series of detritus transport.

Sediment cores collected from Eel deposition on the coastal margin (Drenzek 2009) indicate a

total organic carbon/total nitrogen ratio of ~20, and that terrestrial organic carbon comprises 25-

75% of the sediment carbon. The sediment is mostly lithogenic by mass, but can have high

fractions of biogenic and combustible flux (Walsh and Nittrouer 1999). Particulate organic

matter measured and characterized at the mouth of the Eel River found C:N ratios varying from

10 (at low flows and low POM concentrations) to 15 (at high flows and high POM

Goñiconcentrations) ( et al. 2013). Taken in combination with Drenzek (2009), this implies that

25-50% of the particulate organic nitrogen delivered by the Eel River is relatively rapidly

bioavailable (though some of the uptake presumably occurs on the shelf rather than by plankton

Goñiin the water column). et al. (2013) also directly estimates annual yields of N in 2008 and

2009 as 0.03-0.04% of the total suspended solids. Thus the model estimating “bioavailable

particulate nitrogen held in Eel detritus” as 5% of HydroTrend’s total sediment is a very high

upper bound, while giving us a daily time series that is event-driven by weather conditions. In

the event that the results are nutrient-driven, running experiments that reduced that percentage

could do a better job of estimating it. (This turned out to not be the case, as described in section

3.6 – thus, given this overestimate, it seems very unlikely that Eel nitrogen from detritus has a

significant short-term effect on coastal ocean productivity.)

In summary, the total freshwater discharge entering ROMS from HydroTrend is loaded with a

monthly average dissolved nitrogen concentration based on the USGS data shown in Figure 2.20.

5% HydroTrend sediment mass is added directly as a detritus (particulate nitrogen) input to the

NPZD model. This model does not model other possible micronutrients of interest, such as iron;

discussion of potential methods of iron modeling for future work is found in Chapter 3.11.

Figure 2.22: A graphical representation of the transformation of HydroTrend output into NPZD

nutrients.

83

2.7 Model Experimental Design

Differences between the 10 and 1 km model applications have been mentioned throughout

Chapter 2, and are compiled here for direct comparison. The most significant differences are the

application of an atmospheric formulation, and the vertical mixing parameterization, which had

to be changed at 1 km when the K-Profile parameterization failed to sustain ocean stratification

for any significant period.

Table 2.6: Summary of differences between 10 and 1 km model applications.

Model Differences 10 km ROMS

model

1 km ROMS model

Atmosphere NARR, bulk flux

parameterization

ERA-Interim, direct flux application

Domain 37-47 N, -132-123

W

39 to 42.1966 N, -128.993-123.507 W

Interior Points 275 x 556 374 x 453

Transformation Function 2 1

Stretching Function 4 1

Baroclinic Timestep 180 seconds 30 seconds

Inclusion of Biology No Yes

Inclusion of River No Yes

Initialization dataset ECCO2 10 km results, WOD, WOA

Vertical Mixing

Parameterization

K-profile Mellor-Yamada 2.5

Period of hindcast 1998-2010,

continuous run

2002-2010, 18-month overlapping runs

Spin-up model time 2 years 6 months

The fully-coupled model with a river that estimates Eel River nutrient load was run from 2002-

2010. As a control, the same model without any river was run for the same time period. This

examines the question of does the river matter – by comparing model results with and without

the river we can begin to understand the river’s impact on the coastal environment. Additionally,

to discriminate between whether the nutrient load of the river or the physical presence of the

river was the dominant actor, a zero-nutrient river was run during the year with the largest storm

event (2005-2006). A lack of significant difference between the with-nutrients river results, and

the no-nutrients river results, would indicate that it is the physical effects (eg, the freshwater

plumes) impacting coastal biology, rather than the nutrients delivered by said plumes.

In order to verify that the modeling framework could successfully resolve a nutrient-driven

plume at all, just in case the model itself might be simply failing to connect river nutrients to

ocean biology in some fundamental, mechanistic way, an extra-nutrient river was run for the

same year. Providing 400 times the natural nitrate load of the Eel River to the coastal ocean

should guarantee a biological response; failure to do so would indicate a critical problem with

the modeling framework. Finally, to test the model’s sensitivity to the carbon:chlorophyll ratio

(a possibly major uncertainty discussed in section 2.6), the model was run with double initial

phytoplankton (the equivalent of a doubled choice of C:Chl ratio).

84

Table 2.7: Summary of model experiments.

Model Experiment Years Run

1 km model with river 2002-2010

1 km model without river 2002-2010

1 km model with zero-nutrient river 2005-2006

1 km model with extra-nutrient river 2005-2006

1 km model with double initial phytoplankton 2005-2006

2.8 Model Results

In order to gauge the basic capabilities of the modeling framework to reproduce the physical

system, we consider examples of the time series of HydroTrend discharge and sediment, 10 km

Regional Ocean Modeling System climatologies in summer and winter as well as at short time

scales, and a 1 km ROMS freshwater plume delivered during a storm event.

2.8.1 Results: HydroTrend

We begin by comparing three versions of the HydroTrend model to USGS historical results

(USGS 2012; Syvitski and Morehead 1999; Figure 2.23): what differs is the atmospheric forcing.

Older USGS results are used in order to look at data that includes both discharge and sediment

loads, since the USGS did not continue sediment load measurements into the 2000s. The first

model is forced by a stochastically generated climate based on data from the Eureka Weather

Station of the National Weather Service (National Weather Service 2014). The Eureka National

Weather Service Station (40.81 N, -124.16 W) lacks continuous data necessary to do a

nonstochastic run, but has 1979-2010 monthly averages that were used to construct the climatic

climatologies to generate HydroTrend’s stochastic climate (the method is described in Kettner

and Syvitski 2008).

Additionally, the model is forced by each of two nonstochastic time series, ERA-Interim (Dee et

al. 2011) and the NARR (Mesinger et al. 2006).

Table 2.8: HydroTrend results summary for discharge and sediment. Visualized in Figure 2.23.

Model Description Q

(m3/s)

Qs

(kg/s)

Eureka Weather Station-based stochastic climatology 200 441

NARR nonstochastic time series, 1979-2010 282 446

ERA nonstochastic time series, 1998-2012 280 463

USGS Historical Data (~1995; Syvitski and Morehead 1999) 200 445

The closest results to the USGS Historical Data (which are themselves likely overestimated by

roughly a factor of 2, per Warrick et al. [2014]) come from the stochastically generated climate

using statistics from the Eureka Weather Station. Unsurprisingly, given their additional rain (see

section 2.3.5), extra discharge is created using the NARR and ERA time series. This is

accompanied by more sediment: though the model produces about 140% of the USGS discharge,

it only produces up to 104% of the USGS sediment. As expected, sediment follows discharge

proportionally in both timing and magnitude.

85

To maintain the same atmospheric forcing throughout the modeling framework, it is the ERA

results that must be fed into the 1 km ROMS model. Comparing them directly with USGS

gauging station discharge (Figure 2.24a and 2.24b), HydroTrend successfully captures event

timing, and moderately reproduces event magnitude. The flow generated by the most extreme

storm events is underestimated by about a factor of two, while summer flows and smaller storm

events are overestimated by roughly the same amount, thus spreading the discharge throughout

the year. The underestimation bias of discharge during the major storm events has the potential

to cancel the systematic overestimation overestimation of sediment described in Warrick et al.

2014, such that the sediment time series may be roughly correct during those particularly high-

discharge events.

Figure 2.23: Annual average discharge vs. sediment load for HydroTrend results versus the

USGS validation data. Note that this is a fairly tight cluster far from zero, but zoomed in on both

axes in order to be able to see the differences.

86

Figure 2.24a: ERA-Interim driven HydroTrend vs. USGS gauging data for discharge, 1998-

2010.

87

Figure 2.24b: HydroTrend results vs. USGS data, 1998-2010.


The 10 km resolution ROMS results are not the focus of this study, seeing as they lack any

representation of the Eel River or any biology. However, they provide an excellent

representation of the Northeastern Pacific in heat and momentum, and a brief overview of their

results is presented.

2.8.2.1 Climatological validation

Figures 2.25 and 2.26 contain the major climatological results for the 10 km resolution ROMS

model. They are compared to results from the Simple Ocean Data Assimilation (Carton and

Giese 2008), a 0.25̊ x 0.4̊ x 40 level model forecast that assimilates hydrographic profiles, ship

intake measurements, moored hydrographic observations, and remotely sensed sea surface

temperature. It is well-regarded as a useful set of estimates of ocean circulation, and useful for

comparison. In January (Figure 2.25), sea surface temperature is roughly correct within a

degree, with the caveat that ROMS displays a cooler bias, especially onshore, which disrupts an

otherwise smooth north-to-south temperature gradient. The directional structures of the velocity

fields are well reproduced, with ROMS about a factor of 1.5-2 faster at the various extrema. The

width of the onshore north-flowing current is considerably narrower in ROMS, with the

transition to south-flowing ocean occurring closer to 125̊ W, whereas in SODA this occurs near

126̊ W.

88

In July (Figure 2.26), upwelling is well reproduced, as evidenced by the similarity in onshore sea

surface temperature. ROMS upwelling is considerably more detailed in its shore-following

structure, a reasonable result given its higher horizontal resolution. Offshore, it is about one

degree warmer than SODA. Once again, zonal and meridional velocity structures are well-

reproduced spatially with ROMS momentum greater than SODA's by a factor of two onshore

(and, meridionally, weaker offshore). All in all these results are quite robust; the major summer

and winter features in heat and momentum are clearly being reproduced, making them well

suited for boundary condition forcing in the 1 km model.

89

Figure 2.25: ROMS 10 km results (left) and SODA (right) for sea surface temperature, zonal

(east-west) velocity and meridional (north-south) velocity climatologies for the month of

January, 2000-2010.

90

Figure 2.26: ROMS 10 km results (left) and SODA (right) for sea surface temperature, zonal

(east-west) velocity and meridional (north-south) velocity climatologies for the month of July,

2000-2010.

91

2.8.2.2 Short Time Scale validation

We turn next to an example of shorter timescale validation. Upwelling, though not the focus of

the biological study, often occurs in discrete events throughout the season, as larger gusts drive

Ekman transport. One such event occurred in a roughly 48-hour span around 6/22/2001, on a

clear day with very few clouds. Figure 2.27 compares ROMS results with satellite data from

NOAA’s AVHRR/HIRS sensor (NOAA 2012a). Both the temporal and spatial extent of this

cooler region are well-reproduced, with ROMS’ upwelling event generally 1-2 degrees colder

(and therefore more extreme, in terms of the actual transport of cold deeper waters to the surface;

the model is overpredicting upwelling). This is one example among many of the 10 km ROMS

model’s ability to simulate discrete physical events in the ocean.

Figure 2.27: ROMS vs. satellite sea surface temperature for a 48-hour period around 6/22/2001.

The mouth of the Eel River is starred.

Furthermore, we can consider these results, as well as the climatological results, statistically.

Taylor Diagrams (Taylor 2001) are a readily available tool for this purpose. A modeled field

(ROMS results) is cross-correlated with a reference field (SODA results in Figures 2.25-26, or

for the short timescale validation in Figure 2.27, the AVHRR/HIRS sea surface temperature

sensor), and this value is graphed along the circular axis to the right-hand side of the diagram.

Standard deviations from the mean are graphed along a linear axis. By normalizing the standard

deviations of the modeled fields to the standard deviation of the reference field, it becomes

possible to put modeled variables with wildly different numerical values (such as sea surface

temperature, in Celsius, and U-velocity, in meters per second) on the same diagram.

92

Thus, the “ground truth” (or, in this case, satellite values or SODA values) is at the ‘REF’ point,

or a normalized standard deviation of 1.0, and falls at the very end of the circular axis, with a 1.0

correlation to itself. As modeled values diverge along the circular axis, their goodness-of-fit to

this reference field worsens; when modeled values fall above the normalized standard deviation

of 1.00, their variability is proportionally greater than that of the reference field; below 1.00,

proportionally less.

Figure 2.28: Taylor Diagram for 10 km ROMS results from section 2.8.2.

To interpret Figure 2.28, we begin with the observation that whether at a short or long timescale,

sea surface temperature enjoys the best correlation with the reference fields (of satellite data and

SODA), never less than 0.7. July SST is particularly good, with a cross-correlation above 0.95

93

and a standard deviation essentially identical to that of SODA; January SST has slightly less

variability than SODA, and a correlation near 0.75, while ROMS compares to the satellite results

on 06/22/01 with a correlation of 0.7, but quite a bit more variability across the field. This is

easy to see up in Figure 2.27, where ROMS is, across the domain, both cooler and warmer than

the satellite data in various places.

Velocity is less similar; July V-velocity has a cross-correlation value of 0.6 with SODA, and

that’s the closest they ever come, as cross-correlation values proceed to decline as low as 0.2 for

January V-velocity. They uniformly experience greater standard deviations than the SODA

results. That does not, however, mean that the 10 km results are poor; merely that in velocity

they diverge considerably from SODA results. This is unsurprising. As remarked in section

2.8.1, the increased resolution of the ROMS results compared to lower-resolution SODA (which

is itself a model) has created subtly (and less-subtly) different spatial patterns; while the largest

features of SODA are reproduced, in ROMS they are often in slightly different places, with,

usually, greater intensities. This increase in momentum is most likely the effect of jets and

squirts off the California-Oregon coast, a well-known feature (Strub and James 2000, Keister and

Strub 2008) of the northern California Current that relies on smaller-scale turbulent structures

than SODA simulates.

2.8.3 Model Results: ROMS, 1 km resolution

At 1 km horizontal resolution, the coupled modeling framework includes the Eel River directly.

Figure 2.29 shows a typical example of a storm-driven Eel River freshwater plume, several days

into its delivery and drift. Driven by primarily southerly winter winds, most of the plume

follows the shore northward, its impact felt over 10 km away. However, the plume is also acted

on by features of greater ocean circulation; in this case, an eddy that captures some of the

freshwater, dragging it off to the west. This behavior compares well to the STRATAFORM

project that first observed via cruise, then reproduced via model, plume dynamics as altered by

ocean eddies (Pullen and Allen 2001). The coupled modeling framework thus demonstrates the

ability to simulate freshwater plumes on the daily timescales of the storm event-driven system.

94

Figure 2.29: 1 km ROMS salinity in the coupled modeling framework, producing a river plume

on 12/24/2004. Units are psu. The bottom plot is the same as the top with the colorbar zoomed

in.

95

2.9 Conclusion

In order to examine the effect of Eel River physical and nutrient effects on coastal ocean biology,

a coupled modeling framework was constructed unifying atmospheric forcing, a hydrological

model (HydroTrend), an ocean circulation model (Regional Ocean Modeling System) and a

biological model (NPZD-Powell). Experiments were performed across the 2000-2010 decade,

adding and subtracting the presence of a river with various levels of nutrients. The results of

these tests are discussed in Chapter 3.

A few revelations came out of the construction of the modeling framework: the ERA-Interim

Reanalysis seems unable to correctly capture seasonal temperatures in the Eel River Basin in

Northern California, being both too warm in the winter and too cool in the summer as compared

to Daymet data. Within the Regional Ocean Modeling System, extremely small (~30 second)

timesteps were necessary in order to preserve the CFL criterion at a 1 km horizontal resolution

with the presence of the river. This could be a potentially important constraint on directly

modeling small but extreme rivers in larger regional models. Additionally, the serious and

unsolved problem of three-dimensional ocean circulation modeling being unable to retain

onshore stratification at high horizontal resolutions remained an issue here, and would be a

problem going forward within larger models, as computational expense for model spin-up

increases with model domain.

HydroTrend reproduces time series of Eel River discharge and sediment that compare well to

USGS data in both timing and magnitude. While not a perfect reproduction, it is adequate as a

source for the 1 km Regional Ocean Modeling System’s river, which successfully simulates

freshwater plumes as acted on by local weather and larger circulation features. On a larger scale,

the 10 km ROMS results (used as boundary conditions for the 1 km ROMS simulation)

successfully reproduce the major physical features (i.e. temperature and momentum) of the

northern California Current in both summer and winter. These results are compelling in quality

and may well be useful for providing boundary conditions with a higher horizontal and vertical

resolution than ECCO2 or SODA for other members of the modeling community. Broadly, each

the large components of the coupled modeling framework, atmosphere, river, and ocean,

function well as a physical simulation of ocean circulation.

If the biological results of these experiments (examined in Chapter 3) indicate river-driven

trends, this framework could be nested within global climate models such as the Community

Earth System Model in order to improve river-to-ocean processes, or simply forced forward by

their results offline. As a mesoscale modeling framework that directly simulates the river

(instead of using river data from gauges and cruises), it represents a potentially important

advance in the field of Earth System modeling. The overarching question of the thesis, however,

is whether smaller rivers are of sufficient importance to coastal biology as to make this advance

necessary. To examine this question, we now turn to the biological results.

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Chapter 3: Results

3.1 Introduction

3.2 MODIS validation; coverage and cloud gap-filling

3.3 Climatological comparisons

3.4 Interannual variability comparisons

3.4.1 Correlative analysis of December 2002-2009

3.4.2 Empirical Orthogonal Function analysis of December Interannual Variability

3.4.3 Comparison of Decembers with varying river conditions

3.4.4 Summary of interannual variability comparisons

3.5 Event-driven comparisons

3.5.1 Large river, deep mixed layer

3.5.2 Small river, deep mixed layer

3.5.3 Large river, shallow mixed layer

3.5.4 Small river, shallow mixed layer

3.5.5 Summary of event-driven comparisons

3.6 No-nutrient river modeling

3.7 Extra-nutrient river modeling

3.8 Chl:C sensitivity testing

3.9 Southwestern model artifact and nonlinear model drift

3.10 Discussion

3.11 Future Directions

3.12 Conclusion

3.1 Introduction

In order to search for the potentially small signal (as indicated by Chapter 1) that represents the

Eel River’s effect on coastal ocean productivity, a coupled modeling framework (Figure 2.1) was

created that links hydrological models with ocean circulation models, unified beneath the same

atmospheric forcing. The framework was run across 2002-2010, with a focus on 2005-2006, the

water year with the most dramatic storm-driven Eel River water and nutrient deliveries to the

ocean. The biogeochemical results of these model experiments are presented here.

In order to separate the questions of “does the Eel River have any effect on coastal ocean

productivity” and “is this effect physical or biogeochemical in origin,” two kinds of experiments

were run: comparisons of the fully coupled model to a control that wholly lacks the Eel River,

and comparisons of the fully coupled model to a control that includes an Eel River that lacks any

nutrients. In this way, if the absence of the Eel River leads to significantly different results, but

the absence of Eel River nutrients does not, that implies a physically-driven impact. If the

absence of Eel River nutrients creates a notable effect on the results, that implies that Eel River

nutrient delivery is a significant driver on coastal ocean productivity.

In order to consider the results of the 1 km horizontal resolution ROMS, with inclusion of the Eel

River and the Nutrient-Phytoplankton-Zooplankton-Detritus biogeochemical model (Powell et

al. 2006), three timescales are considered in the search for effects of the Eel River on coastal

ocean productivity. First, monthly climatologies constructed from the entire 2002-2010 results

97

are constructed and compared between the fully coupled model and the no-river control. As

most river delivery events happen on weekly or daily timescales rather than monthly, it is not

wholly surprising that the possible signal of riverine nutrient-driven ocean productivity is not

well-resolved here. However, possibilities of accumulative effects (such as the sinking of river

nutrients below the euphotic zone, upwelled later in the year) make the climatological

examination potentially interesting.

Second, interannual variability is considered, specifically during the often high-discharge month

of December. After initial correlative studies of phytoplankton concentration, mixed layer depth,

surface stress, mean river discharge and shortwave radiation flux fail to indicate strong

relationships, Empirical Orthogonal Functions (Bjornsson and Venegas 1997) are constructed to

describe the set of eight consecutive December results, and their behavior compared to possible

drivers including the Pacific Decadal Oscillation (Mantua 2014), the Oceanic Niño Index

(NOAA 2014b), and Eel River discharge (USGS 2012). Finally, three Decembers of notably

different Eel River behavior (“high flow” in 2005, “average flow” in 2003, “minimal flow” in

2008) are examined directly. While the model reproduces phytoplankton dynamics fairly well in

timing and magnitude (though not spatial extent), evidence of riverine impact is small.

Finally, in an effort to more clearly resolve riverine effects, analysis turns to event-driven

impacts, which is to say the largest Eel River discharge event of each water year. These vary

greatly in timing and magnitude, and the state of the coastal ocean varies greatly as well,

dominated by seasonal behavior. River plume behavior is inconsistent, seemingly overpowered

by the state of the ocean at time of delivery, as highly turbulent oceans mix the river plume

rapidly, while relatively stable oceans can support a freshwater plume across its surface for

greater distances. In this case as well as the former two, to the extent that the Eel River appears

to have an impact, it is a repressive, rather than positive, effect on phytoplankton growth, as the

Eel River’s relative lack of nitrate compared to the coastal ocean appears to suppress growth.

Each of these timescale analyses is considering the overall effect (or lack thereof) of the modeled

Eel River as compared to the no-river control. River nutrient effects are examined directly by

looking at both the no-nutrient river control and an extra-nutrient river experiment. The latter is

performed in order to demonstrate that the modeling framework has the ability to resolve river

nutrient-driven phytoplankton growth at all, given the lack of effect under realistic conditions.

Throughout each of these analyses we acknowledge concern about model uncertainty; this is

discussed in depth in its own section. Possible drivers of uncertainty include the unknown and

variable Chlorophyll:Carbon ratio, boundary condition-created numerical noise, and model drift

from the nonlinear differences between runs with and without the presence of the river. The

framework also only considers nitrogen; the possibility remains that another micronutrient such

as iron is the riverine nutrient delivery that has an impact on coastal ocean primary productivity.

After discussion of the model results, possible future directions for this line of research are

presented.

98

3.2 MODIS validation; coverage and cloud gap-filling

Using satellite imagery for validation, particularly in so cloudy a part of the world as coastal

Northern California, comes with inevitable interference. It is vital that the cloudiness of these

images be considered thoroughly, in order to recognize which graphics are truly robust for

validation purposes, and which run the risk of creating false negatives. Throughout this work we

use regridded MODIS Aqua satellite data (NASA 2013) that has been reprocessed by Oregon

State University cloud gap-filling algorithms (OSU 2014). These algorithms replace missing

pixels by searching an expanding zone around that pixel, looking for data. All points found in

the zone are averaged together for the replacement value. There comes a point, however, where

it is better to search forward and backwards in time (+/- 8 day averages, each of which is itself a

composite of multiple images across those 8 days) than to search further and further away

spatially; this algorithm defines that point as beyond an 80 km distance, and interpolates data

accordingly. (The full white paper describing this algorithm is available online, OSU 2014). But

how many gaps are being filled? And how big are the gaps?

MODIS monthly averages have excellent coverage in our region of interest; the November-June

climatologies used in section 3.3 never have an average coverage less than 97% (eg, 3% missing

pixels because of clouds), with an absolute minimum of 91% in January 2010. No gap-filling is

necessary at all; however, that’s because this NASA product simply averages every non-missing

value for each pixel present, and manages to get at least one value for essentially every pixel at

least once a month. This has an obvious problem: a bloom present in a pixel on one day, when

all other values of that pixel throughout the month are covered by clouds, may not in fact persist

throughout the month – nor might the absence of a bloom persist.

Table 3.1: Average over-ocean chlorophyll-a satellite coverage in the 39.5-41.5 N, 123-125 W

region of interest near Cape Mendocino for the November-June 2002-2010 climatologies.

2002-2010 November December January February March April May June

Average

Coverage

99.3% 98.9% 98.1% 97.6% 98.2% 98.6% 97.4% 97.9%

The Decembers of interest in section 3.4 (2003, 2005 and 2008) are each composed of 4-5

MODIS 8-day average snapshots. Once again the coverage is often very good, though

occasionally poor. It is often the case that adjacent 8-day averages will be sufficiently different

(‘very good’ coverage next to ‘clouds everywhere’ coverage) that much of the gap-filling is

occurring temporally instead of spatially. December 2005 has little coverage because of the

extraordinary storms in that period. It is thus possible that the good agreement between model

and ‘data’ late in the month is a false positive; however, what they are agreeing on is that there is

very little phytoplankton growth, which is consistent with very little sunlight.

99


region of interest near Cape Mendocino for the 8-day averages within December 2003, 2005 and

2008.

Weeks of

2003

Average

Coverage

Weeks of

2005

Average

Coverage

Weeks of

2008

Average

Coverage

12/01/03 84.4% 12/01/05 83.8% 12/01/2008 98.3%

12/10/03 46.6% 12/10/05 98.2% 12/10/2008 99.5%

12/17/03 60.8% 12/17/05 55.5% 12/17/2008 99.5%

12/24/03 98.6% 12/24/05 3.2% 12/24/2008 24.8%

12/29/03 16.1% 12/29/05 71.4% 12/29/2008 91.8%

Finally, the largest river discharge events in each year described in section 3.5 have a widely

variable range of coverage. It is not unusual to have poor coverage within one 8-day average of

the event, and despite fears that the clouds that generated this discharge event would mask the

satellite coverage, is never poor throughout the entire period. Helpfully, the year with the worst

coverage, 2005-2006 (again coinciding with the problematic coverage in the December analysis)

has its best coverage of the three, above 70%, on the actual averaged 8-day period of the 2005

event itself. Its gap-filling is thus spatial rather than temporal, and what it fills with is ‘very little

phytoplankton present’ as the consistent behavior of the region.


region of interest near Cape Mendocino for the 8-day averages surrounding each of the largest

Eel River discharge events in the 2002-2009 water years. (The event falls in the second of three

8-day averages in all years.)

2002/03

Event

Average

Coverage

2003/04

Event

Average

Coverage

2004/05

Event

Average

Coverage

12/09/02 78.6% 02/10/04 91.7% 05/10/05 91.1%

12/16/02 6.5% 02/18/04 60.4% 05/19/05 96.9%

12/23/02 75.2% 02/25/04 60.5% 05/26/05 95.2%

2005/06

Event

Average

Coverage

2006/07

Event

Average

Coverage

2007/08

Event

Average

Coverage

12/24/05 3.2% 12/23/06 5.2% 12/30/07 26.0%

12/29/05 71.4% 12/31/06 83.9% 01/05/08 25.3%

01/07/06 11.0% 01/07/07 87.1% 01/13/08 58.5%

2008/09

Event

Average

Coverage

2009/10

Event

Average

Coverage

02/25/09 18.9% 01/18/10 53.8%

03/03/09 69.5% 01/26/10 70.0%

03/11/09 97.1% 02/04/10 72.9%

In order to digest the representativeness of these averages to represent phytoplankton blooms, we

must also consider the timescales of the blooms themselves. Bloom duration is widely variable,

with relevant environmental variables including light availability, nutrients, temperature, and

100

stratification of the water column, as well as initial phytoplankton stock size (Mann and Lazier

2007). Fully characterizing typical growth and decline rates of open-ocean phytoplankton

around Cape Mendocino would require ‘ground truth’ data that does not exist, ideally taken by

moored chlorophyll concentration sensors. This is, however, an opportunity for models to

attempt to characterize the unknown. Although the model results presented in Chapter 3 are

always 8-day averages, in order to match up with the satellite data, model results were calculated

every 30 seconds, and collected daily. By studying the daily time series of phytoplankton

growth and decline within a given grid cell, we can consider rates of change within our system,

and what might be lost by the satellite snapshots and averages. A full analysis of time variability

of phytoplankton in the region, as modulated by phytoplankton depth within the water column, is

beyond the scope of this work (though an interesting future direction). Instead, the two figures

below demonstrate typical examples of daily-timescale fluctuations.

Figure 3.1: Daily averaged values of phytoplankton concentration in the first week of December

2004, taken at 40.5 N, -124.5 W, at the sea surface and at 10m depth.

In the winter, model phytoplankton concentrations are small. The fluctuations are also small, but

are often rapid; this is a typical example of a distinct increase and decline in growth, followed by

a slower increase. If a satellite took snapshots of this cell 12/2 and 12/8, it would essentially

miss much of the internal variability; a snapshot on 12/4, taken alone, could falsely characterize

the 10m depth concentration as higher than it is the rest of the time.

12/02/04 12/04/04 12/06/04 12/08/040

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

Daily Phytoplankton Variability, December 2004

Sea Surface

10m Depth

Day

mg

ch

la/m

3

101

Figure 3.2: Daily averaged values of phytoplankton concentration in the first week of July 2004,

taken at 40.5 N, -124.5 W, at the sea surface and at 10m depth.

In the summer, modeled blooms are more gradual in their growth and decline, and larger in

magnitude. However, occasional daily-timescale fluctuations are not unknown; the minimum on

5/3/04 at the sea surface is not atypical. Coverage is often better in summer, particularly if the

satellite passes overhead in the afternoon after the fog has burnt off; but conversely averages are

sometimes more representative, given the smaller rates of change involved with these dense

phytoplankton blooms.

There is a very real possibility that much of the difference between MODIS data and model

results lies in the differences in their averaging (as MODIS averages once or twice within an 8-

day period, likely sometimes entirely missing phytoplankton variability, while the model

averages 8 daily-averaged timepoints). Furthermore, MODIS cannot always provide good

coverage, and while cloudiness begets light-limitation and thus low concentrations of

phytoplankton, sometimes the gaps that need to be filled are sufficiently large that MODIS ‘data’

is more of a best guess as to what’s in the ocean. Fortunately, within our region of interest,

satellite coverage is usually above 60%, and often above 80%. Finally, MODIS is this project’s

05/02/04 05/04/04 05/06/04 05/08/040

1

2

3

4

5

6

7

8

Daily Phytoplankton Variability, July 2004

Sea Surface

10m Depth

Day

mg

ch

la/m

3

102

validation of choice because it is essentially the only option; there is no alternative! It is

commonly and widely used, but perhaps dangerously so. The field has a real need for more

moored, stationary measurements of phytoplankton growth and decline over time in order to

understand the ability of occasionally captured, time-averaged satellite pictures to describe these

environmental systems.

3.3 Climatological comparison

Figures 3.3 to 3.5 (shown at the end of this section) summarize monthly climatological results,

comparing the fully coupled modeling framework (left) to MODIS results (middle; NASA 2013)

to a subtraction of the model results from the no-river control results, vertically integrated across

the water column (right).

The magnitude of late Fall/early Winter onshore blooms is generally well-reproduced by ROMS

during the winter months, at about 2 mg chlorophyll per cubic meter. Unlike in the MODIS data,

however, blooms are strongly concentrated to the south rather than the north of the cape. In

February, there is a sharp increase in model production by about 50% that is unmatched by the

data, but in March, as upwelling begins, magnitudes are again similar. ROMS upwelling-driven

productivity appears to occupy a much wider spatial band than MODIS, and fails to concentrate

north of the cape. In April and May, ROMS productivity also fails to keep up with MODIS-

reported production, underestimating by about 50%. These large differences force us to treat all

further discussion of the model with due caution, particularly as pertains to upwelling. As the

major river discharge occurs outside of upwelling months, however, there is still potentially

insight to be gleaned.

If one expected the presence of the river in the model to stimulate production during the winter

months of most extreme Eel River discharge (November-January), the ROMS results show

almost totally opposite behavior. In November, the model with the river shows a minor average

increase in productivity north of the cape, but south of the cape, as well as onshore in December

and January, productivity appears to be slightly suppressed in the model with the river as

compared to the control without. Starting in February, the presence of the river appears to

slightly stimulate onshore production north of the cape. In April, however, with upwelling

season often in full swing, there is both an increase in river-driven productivity far south of the

cape, as well as a decrease around the cape's head. Finally, in May, the presence of the river in

the model seems to allow for more onshore productivity, both north and south of the cape, but

especially to the north, in the area of typical plume deposits.

The magnitude of all of these monthly averaged differences, however, is small, however,

compared to the total chlorophyll: it is necessary to vertically integrate the water column in order

to resolve them, and they account for only 7%-13% of the total chlorophyll present. Many of the

differences are difficult to unpack from the scale of model uncertainty; as discussed in section

3.9, behavior south of the cape, in particular, is heavily impacted by boundary condition-driven

numerical noise. The next two sections will show that in general, the slight suppression of

phytoplankton production onshore during river-dominated months is consistent with nitrate

limitation within plume-affected parts of the water column. The most potentially significant

difference, the stimulated production in May (Figure 3.5), might be the signature of the “shelf-

103

capture nutrient capacitor” hypothesis (Chase et al. 2007), the concept that river nutrients sink

out of the euphotic zone uneaten, then enhance productivity when subsequently upwelled later in

the year. However, there was no indication that detritus (the slowly remineralizable nutrient in

the model, and the one that might behave in this manner) accumulated over the winter on the

shelf in such a manner as to explain this behavior. The source of the additional productivity in

May is thus unclear.

To speak to these climatologies in a statistical framework (summarized in Table 3.4 below), a

Taylor diagram (Taylor 2001) as used in section 2.8.2 might be appropriate, except that the

pattern cross-correlations are dominated by the model artifact. It is easy to see in these figures

that MODIS predicts stronger northward blooms, while the ROMS artifact lies to the south; thus,

the cross-correlations are uniformly negative. The normalized standard deviations of the model

as compared to MODIS are somewhat more interesting. Recall that for normalized standard

deviations, a value of 1 indicates that the model result variability is equal to the satellite data

variability. In November, December, January, February, May, and June, the model with the river

exhibits variability more similar to MODIS than the model without; this does not hold for March

and April. In the winter months, the model is overly variable as compared to MODIS; this

reverses in spring, with the advent of upwelling, which is as noted previously not well-

reproduced in the model’s biological response.

Table 3.4: Pattern cross-correlation values (R) and normalized standard deviations for the

November-June model climatologies (2002-2010) as compared to MODIS climatologies over the

same period.

Model R Ratio =

var(model)/var(sat)

November Climatology w/River -0.13 1.6513885753

November Climatology w/o River -0.04 1.9936780312

December Climatology w/River -0.25 1.1220779221

December Climatology w/o River -0.225 1.3428571429

January Climatology w/River -0.413 1.1531531532

January Climatology w/o River -0.409 1.4774774775

February Climatology w/River -0.322 1.7080924855

February Climatology w/o River -0.463 1.9161849711

March Climatology w/River -0.207 0.6755373593

March Climatology w/o River -0.399 0.747185261

April Climatology w/River -0.292 0.4810539523

April Climatology w/o River -0.3008 0.5803011292

May Climatology w/River -0.316 0.2946175637

May Climatology w/o River -0.46 0.2507082153

June Climatology w/River -0.46 0.2077294686

June Climatology w/o River -0.59 0.1542540371

104

Figure 3.3: ROMS chlorophyll climatologies (A, D, G), MODIS (NASA 2013) chlorophyll

climatologies (B, E, H), and the ROMS climatology integrated vertically across the water

column, for water years 2002-2010, with the no-river model control subtracted off (C, F, I).

Monthly climatologies are sorted by row for November (top), December (middle) and January

(bottom). Units are mg chl-a per cubic meter (square meter, in the case of the integration).

105

Figure 3.4: ROMS chlorophyll climatologies (A, D, G), MODIS chlorophyll climatologies (B, E,

H), and the ROMS climatology integrated vertically across the water column, for water years

2002-2010, with the no-river model control subtracted off (C, F, I). Monthly climatologies are

sorted by row for February (top), March (middle) and April (bottom). Units are mg chl-a per

cubic meter (square meter, in the case of the integration).

106

Figure 3.5: ROMS chlorophyll climatology (A), MODIS chlorophyll climatology (B), and the

ROMS climatology integrated vertically across the water column, for water years 2002-2010,

with the no-river model control subtracted off (C). Climatologies are for the month of May, the

latest month in which significant Eel river discharge is found to ever occur from 2000-2010.

Units are mg chl-a per cubic meter (square meter, in the case of the integration).

3.4 Interannual Variability Comparisons

In order to consider interannual variability of coastal ocean productivity as potentially driven by

riverine impacts, the set of December results from 2002-2009 is analyzed correlatively, as well

as direct comparisons of specific years of interest that span a range of river conditions.

3.4.1 Correlative analysis of December 2002-2009

The balance between nutrients and light drives the biology of phytoplankton in the mixed layer.

As winter sets in, turbulence deepens the mixed layer, increasing its nutrient concentration but

also the amount of time that phytoplankton spend below the euphotic zone. When the mixed

layer shallows, there is an opportunity for growth dependent on these nutrients, until they

become depleted (Mann and Lazier 2006).

The model's behavior in December reproduces this basic premise. A station at 40.65 N, -124.36

W (which is five kilometers north of the modeled river channel, with an ocean depth of 290m) is

examined across all Decembers. As Table 3.5 shows, in 2002, 2005, 2006 and 2008, a relatively

shallow mixed layer is already present at the beginning of the month along with a phytoplankton

maximum, and phytoplankton concentration declines as the mixed layer deepens with the onset

of winter storms. In 2003, 2004, and 2009, phytoplankton concentration increases in mid-

December as the mixed layer shallows. And in 2007, phytoplankton concentration is markedly

lower throughout the month compared to all other years, and declines throughout the month

independently of mixed layer depth.

107

Table 3.5: December mixed layer depths and maximum phytoplankton concentrations at 40.64

N, -124.36 W, ocean depth 290m.

Year-Day

of year

Mixed

Layer

Depth (m)

Maximum

Phytoplankton

Concentration

(mmol-N/m3)

2002-337 21 3.3

2002-345 40 2.75

2002-353 40 2.6

2002-361 40 1.7

2003-337 40 2.65

2003-345 10 4.1

2003-353 10 5

2003-361 21 4.74

2004-337 21 2.25

2004-345 14.5 5.1

2004-353 10 1.7

2004-361 21 3.75

2005-337 14.5 6.9

2005-345 14.5 6.9

2005-353 112 1.56

2005-361 80 1

2006-337 14.5 6.3

2006-345 21 5.25

2006-353 28 3.6

2006-361 14.5 3.4

2007-337 60 1.05

2007-345 28 0.66

2007-353 28 0.66

2007-361 40 0.32

2008-337 10 5.3

2008-345 10 3.25

2008-353 14.5 2.8

2008-361 21 2.8

2009-337 14.5 1.5

2009-345 10 4.25

2009-353 10 5.1

2009-361 10 4.3

Average 26.359375 3.329375

Figure 3.6 (below) plots a variety of potentially relevant parameters to phytoplankton

concentration against each other. Surface stress (from strong winds) deepens the mixed layer

through generation of turbulence; shortwave radiation flux provides (or limits) the light on which

the phytoplankton can grow; if mean river discharge were strongly correlated with any quantity,

that would of course be compelling, and mixed layer depth and phytoplankton concentration are

108

also plotted directly. In no cases is the R2 value significant. However, as these data points are

created by (and potentially controlled by) different conditions from year to year, we can still

glean some insight by examining what patterns exist within the plots.

Figure 3.6.E shows the December relationships between mixed layer depth and phytoplankton

concentration. While phytoplankton concentrations vary widely in the shallow mixed layer, the

higher concentrations (3 mmol-N/m3) are only reached in shallow conditions. Note that for the

purposes of this study, mixed layer depth was defined as the lowest point of near-constant

phytoplankton production, before it sharply falls off in response to physical stratification.

The most rudimentary expectation of the application of freshwater coastal runoff to the ocean is

that runoff will make the surface layer more buoyant, preventing mixing, and thus, in light-

limited conditions, produce a bloom by increasing the amount of light that phytoplankton in the

mixed layer receive on average (Mann and Lazier 2006). However, Figure 3.6.B demonstrates

the opposite behavior: in the seven cases of mean river discharge above 20,000 cubic feet per

second, five coincide with conditions at or above the 78th percentile of mixed layer depth (thus

comprising 5/8ths of the 78th

percentile, as there are 8 cases total); these same five cases have

phytoplankton concentrations well below average for the month (Figure 3.6.D).

Deeper (40+ meters) mixed layers universally coincide with below-average shortwave radiation

(more clouds; see Figure 3.6.C), and near-universally with higher surface stress (more wind; see

Figure 3.6.A) which, when considered in combination with the timing of discharge, is equivalent

to saying that the same storm events that produce Eel plumes are also deepening the mixed layer

through turbulence. Thus it appears the effect of the deeper mixed layer dominates the

biogeochemistry of the water column, as compared to the effect of the river plume. Another

reason plumes may fail to significantly buoy the mixed layer is thermal: in December, the

modeled Eel River delivers a plume of 9.6 degrees Celsius (see Chapter 2.5.11), but average sea

surface temperature is nearly 9.8 Celsius, and can range as high as 11.8. This further offsets the

effect of the lower salinity by increasing plume water density. Furthermore, the location of the

station at which this data are collected and compared is 5 km north of the Eel River mouth,

meaning that the plume it sees has transported (and entrained ocean water) over a considerable

distance. This was deliberate, in order to separate these events out from the effect of low-level

continuous delivery of seawater to the ocean, but it does mean examination of specifically far-

field plume effects. Finally, timescale is a consideration: due to the comparison to the MODIS

8-day averages, the most extreme, short-term behavior is lost, if a given plume is only in play for

one or two days in a snapshot of eight; much of its momentary effect is averaged away in the

results we see. For further discussion of buoyancy and river plume anatomy, see section 3.10.

109

Figure 3.6: Correlations between mixed layer depth and A: surface stress, B: mean river

discharge, C: shortwave radiation, and E: phytoplankton concentration, as well as phytoplankton

concentration vs. D: mean river discharge and F: shortwave radiation flux.

110

3.4.2 Empirical Orthogonal Function analysis of December Interannual Variability

Taking the eight Decembers as a single time series and applying empirical orthogonal function

analysis (summarized in Figure 3.7, left), we find a strong resemblance between EOF 1 and the

climatological mean (previously shown in Figure 3.3), including anomalous blooms to the south

of the cape. EOF 2 further captures this behavior, maximized right over the problematic

Mendocino scarp (discussed in section 3.9). It is reasonable that the largest EOFs bear little to no

resemblance to the riverine signal sought after. Chapter 1 demonstrated in detail that whatever

impact the Eel River has on coastal ocean productivity, it is small, largely overpowered by other

processes.

And after removing those two larger modes, EOF 3, accounting for nine percent of the

variability, is a clearly northern signal, centered near the mouth of the river. 9% is a similar

magnitude to the climatological impact of the river on water column productivity in section 3.3.

Upon examination of the time amplitudes of each of these functions (Figure 3.7, right), the third

bears some resemblance to the time series of river discharge (Figure 3.8.A), with its consistently

positive anomalies in the first half of the decade, and consistently negative anomalies in the

second half. The El Niño Southern Oscillation is a large signal capable of governing interannual

variability, charted by NOAA 2014b and reproduced here in Figure 3.8.B; while it bears some

resemblance to EOF1, they lack sufficient coherency to readily attribute the variability there.

Similarly, the Pacific Decadal Oscillation, charted by (Mantua 2014) and reproduced in Figure

3.8.C has some coherency with EOF3 in the first half of the decade, but ceases to be a good

predictor over the entire decade.

Across these last two sections, it is very difficult to find strong correlations between river

discharge and coastal ocean productivity. Model artifacts dominate much of the behavior,

particularly offshore and south of the cape; still, it is possible that the river drives a smaller mode

of variability. Near-shore (such as the station studied in 3.4.1) behavior appears to be driven by

many different forces, with riverine impacts largely subsumed by the effect of the mixed layer

depth, as deepened by the storm events that created river discharge in the first place. Given the

great interannual variability in conditions, and the relative lack of insight gained statistically, the

next step to improve understanding is to look at particular Decembers in years of interest.

111

Figure 3.7: The first three empirical orthogonal functions of the 32-point time series comprised

of four 8-day averages per December from 2002-2009, and their variation in time of amplitude.

112

Figure 3.8: 8-day averaged time series of Eel River discharge (A), annual Oceanic Niño Index

(B) and Pacific Decadal Oscillation (C) for December 2002-2009. Red and blue bars are positive

and negative anomalies respectively; for discharge, above and below the mean value line

(~20,000 cfs).

113

3.4.3 Comparison of Decembers with varying river conditions

To look more closely at possible effects of the river in December, 2003 (moderate discharge),

2005 (extreme discharge) and 2008 (minimal discharge) provide a wide variety of conditions.

As Figure 3.9 demonstrates, 2003 had discrete discharge events spread throughout the month, on

December 7, 11, 14, 21, 25, and 30. 2008 had minimal discharge until December 22, and then

three very modest discharge events before the end of the month. 2005 begins with a discharge

event on December 2, and then has minimal discharge until December 19, during which

discharge is continuously elevated and reaches the maximum of the entire decade on December

31. 2003 and 2005 also have out-of-phase discharge events during the first two thirds of the

month, further increasing their potential for comparison.

Figure 3.9: Daily mean Eel River discharge for December 2003, 2005 and 2008.

These Decembers also have markedly different phytoplankton timing and magnitudes. Figure

3.10 shows the estimates of chlorophyll-a concentration as seen by MODIS. In 2003, a distinct

bloom arises, then fades, in the middle two weeks of the month. In 2005, the chlorophyll is at its

maximum at the beginning of the month, then declines. And in 2008, an initial chlorophyll

bloom fades to minimal activity by the third week, only for a new bloom to appear at the end of

the month.

The timing of the 2003 bloom coincides well with the maximum river discharge (and a general

period of river activity), but river discharge at the end of the month does not cause the bloom to

sustain. In 2005, a river event occurs at the beginning of the month, coinciding with the

phytoplankton maximum, but the decline thereafter accelerates as the extreme discharge arrives.

114

And in 2008, the initial bloom is clearly river-independent, but the final bloom does coincide

with the small discharge events at the end of the month. But is this a real connection, or only

coincidence? To examine possible effects of the river during this period, we turn to the model

results.

Figure 3.10: 8-day average chlorophyll-a concentrations as seen from space by MODIS (NASA

2013) for Decembers of interest: 2003, 2005 and 2008. The mouth of the Eel River is starred.

115

Figures 3.11, 3.12 and 3.13 show the model's reproduction of each of these respective years, with

chlorophyll mapped horizontally for direct comparison with MODIS (Figure 3.10). In order to

closely examine possible physical effects of the river, a vertical transect in phytoplankton,

salinity, temperature and meridional velocity is taken at 40.64 N, five kilometers north of the

river channel, with the no-river model control subtracted from the fully coupled modeling

framework. Overall, the model roughly reproduces the timing and magnitude of bloom

dynamics in 11/12 of these timepoints – the bloom appears at the right time, with roughly the

right magnitude -- with the single major difference being the 2008 bloom that initiates in the

week of December 24th

, which is not produced by the model at all. Notably, the model tends to

produce a bloom south of Cape Mendocino which is not present in the data (produced by the

southern boundary artifact described in Chapter 3.9), and the blooms north of the cape often

persist further offshore than the data would indicate.

116

2003

Figure 3.11: 8-day averaged model results for December 2003. A: Chlorophyll at 4m depth

produced by the fully coupled modeling framework. B-E: Vertical transect of the model at 40.64

N, out to 10 km offshore, with the no-river control subtracted from the full model, for

chlorophyll (B), salinity (C), temperature (D) and meridional velocity (E).

In 2003, the model correctly simulates little phytoplankton production in the first week of

December, and then a roughly accurate bloom in the second. In the MODIS results, that bloom

is in decline and isolated north of the cape in the third week, but in the model it is reaching its

maximum, and is distributed both to the north and south of the cape, consistent with the

climatological tendency for the model to concentrate blooms south of the cape that are not

present in reality. Interestingly, though the bloom begins to decline, it retains a clear presence in

the fourth week, whereas in reality it has been reduced to nearly zero. Still, in the time

117

derivative sense, the model is capturing the MODIS data’s increase and subsequent decrease of

phytoplankton, only more slowly. Statistically speaking, the cross-correlation value begins very

positively, then declines throughout the month as the model results retain a bloom that has

vanished within MODIS. The model variability overestimates MODIS variability throughout

December 2003, but much more extremely in the latter half of the month with the persistent

bloom. The often extreme differences in R values between the model with and without the river

included are explained by the presence of the model artifact to the south of the cape; noise

essentially random in nature, the artifact providing more or less concentration at a given time

point can substantially alter the similarity of the model field to MODIS.

Table 3.6: Pattern cross-correlation (R) values and normalized standard deviation comparisons

between December 2003 model results and MODIS data.

Model and week within

December 2003

R Normalized standard

deviation

1st week, w/river 0.529 1.2791666667

1st week, w/o river 0.576 1.5416666667

2nd

week, w/river 0.02 1.184

2nd

week, w/o river 0.008 1.344

3rd

week, w/river -0.398 2.5

3rd

week, w/o river -0.348 2.4285714286

4th

week, w/river -0.04 12.6666666667

4th

week, w/o river 0.3 12.6666666667

Vertically, even though the river has yet to have a major discharge event in the first week, there

is the presence of a layer of slightly warmer, lower-salinity water in which there is slightly more

phytoplankton than in the model sans river. At about -124.4 W, four kilometers offshore, the

mixed layer in the no-river control is warmer, with a bloom that is not present in the with-river

version. The meridional velocity flows more strongly to the north beneath this more distinct no-

river thermocline.

In the second week, the effect of the river is visible, with lower-salinity water appearing to

concentrate onshore and penetrate outwards in a layer up to 200m deep with a minimum salinity

closer to 100m depth. The positive temperature anomaly caused by this layer relative to the no-

river control is roughly twice as strong as the previous week, and phytoplankton grow to double

the magnitude of the no-river control. This effect is near the surface within three kilometers of

shore, with a second positive anomaly at eight kilometers and 150m depth, neatly following the

low-salinity plume. The difference in meridional velocity is similar to the previous week, and

though it is slightly intensified and elevated in depth, it is difficult to tell if this was induced by

the river or simply a longer-term physical (or numerical) difference (see section 3.9). In the third

week, this warmer low-salinity layer persists (if lessened in magnitude), and the bloom has

intensified, particularly at the surface of the water column. Meridional velocity in the no-river

control is now markedly stronger than in the fully coupled framework, in a layer of up to 200m

depth.

118

The effect of the river declines in the final week, along with the expected reversal of the bloom

anomaly; keeping in mind that this bloom has already declined much further in the MODIS data,

it exists more strongly in the model without the river than in the one with it. The lower-salinity

water onshore has nearly returned to pre-significant river discharge differences, with negligible

differences in temperature. The momentum anomaly has also declined, though it retains its

negative bias.

119

2005





In 2005, the model reproduces the northern bloom present at the start of the month, which

declines both spatially and temporally as indicated by the MODIS results. There is an offshore

southern bloom consistent with the climatological anomaly, and it declines as well. R values

improve throughout the month as the presence of the bloom (and its model artifact-driven

concentration to the south of the cape) declines. However, even at its best in the fourth week, the

model exhibits three times as much variability as the MODIS data. This can be taken with

120

caution, however, since in both cases it is comparing values very near zero (as little is going on

in either the model or the results).




December 2003


deviation

1st week, w/river -0.06 1.8214285714

1st week, w/o river -0.56 2.1071428571

2nd

week, w/river -0.2 2

2nd

week, w/o river -0.42 2.2162162162

3rd

week, w/river -0.05 1.7142857143

3rd

week, w/o river 0.21 1.2857142857

4th

week, w/river 0.18 2.875

4th

week, w/o river 0.22 2.75

With the river present (and there is a significant river discharge at the beginning of the month),

the mixed layer at the surface has a stronger phytoplankton bloom than is present in the control

(though it must be remembered that all of these magnitudes are very small). This layer has

slightly lower salinity and is up to 1 degree warmer, with a now positive momentum anomaly.

Its strength is partially, but not entirely, due to longer-term model differences than the discrete

river event.

Throughout the next three weeks, the surface of the mixed layer remains warmer and lighter due

to the presence of the river, with the low-salinity layer expanding further offshore and down to

100m depth. Although the mixed layer retains a heat anomaly and salinity anomaly near the

surface, it is also deepening (presumably due to the extreme storm events throughout the second

half of the month), and this river-driven anomaly cannot counterbalance that past the second

week (when it does, indeed, appear to cause a phytoplankton bloom that is otherwise both lower

concentration and more diffuse throughout a deeper mixed layer in the no-river control). By the

third week there is if anything more phytoplankton occurring without the river present,

particularly near the surface; the magnitude is a fifth of the positive effect earlier in the month.

And in the final week, despite the extreme river discharge, the phytoplankton is functionally

identical throughout the water column, and near zero. The positive momentum anomaly

coincides with the initial river event, and again at the end of the month, but does not seem

spatially correlated with the surface low-salinity layer from the river.

121

2008





In 2008, the model reproduces a bloom that exists in the first week of December and declines

through the third, with the usual concentration south of the cape (as reflected in the negative R

values provided in Table 3.8). However, MODIS displays a bloom in the final week that is

simply not present in the model, which coincides with the first elevated river discharge in the

2008-2009 water year. The normalized standard deviations, unusually, tend to underestimate

MODIS variability early in the month, before overestimating them in the third week and

matching them well in the fourth.

122




December 2003


deviation

1st week, w/river -0.15 0.2842465753

1st week, w/o river -0.19 0.2431506849

2nd

week, w/river -0.31 0.9146341463

2nd

week, w/o river -0.28 0.6707317073

3rd

week, w/river -0.31 4.9090909091

3rd

week, w/o river -0.39 4.0909090909

4th

week, w/river -0.09 0.9285714286

4th

week, w/o river -0.04 0.9821428571

As the first three weeks in 2008 exhibit minimal river discharge, this provides us with an

opportunity to estimate the approximate magnitude of minimal river discharge-driven nonlinear

model drift from the no-river control up until, and throughout, the month of December. The

phytoplankton are similar throughout the first week, with a small positive bias in the surface in

the first week becoming an equally small negative bias by the third. There does appear to be a (-

0.2 psu) low-salinity layer present at up to 75m depth, which declines, then inverts to a (+0.1

psu) positive-salinity in the third week. The heat also goes through transition; the mixed layer is

up to 1 degree warmer, particularly offshore, in the fully coupled model, and 1 degree warmer in

the no-river control by the third week. The extremity of this effect makes it very difficult to

justify significant conclusions about heat-driven dynamics in other model years, as they are of

the same order of magnitude of the anomalies in 2003 and 2005.

In momentum, the no-river control has a stronger northern current along the surface, which

declines throughout the month, including when the river appears in the fourth week, and is

unlikely to be a true river impact. However, when the river does appear (easily visible within

three kilometers of the coast in the salinity anomaly), there is no apparent effect to the

phytoplankton in the model. It is delivering the usual elevated concentrations of detritus and

nitrate; the "missing bloom" in the fourth week of December is, perhaps, being driven by some

other phenomena. The model mixed layer is deepening throughout the month; it is also possible

that it is failing to capture a physically-driven bloom in the fourth week, but as the fourth week

coincides with mixed layer-deepening storm events, that seems less likely.

3.4.4 Summary of interannual variability comparisons

In both December 2003 (average river discharge) and 2005 (extreme river discharge), for each 8-

day average taken across the vertical transect, there is the presence of a low-salinity, warmer

layer of water (which in turn is present at the same time as the first riverine deliveries in each

December). Within these layers (e.g., within the plume), the model with the river has up to 40%

more phytoplankton concentration than the no-river control. In 2005, at the end of the month

(which is when the most extreme riverine delivery of the decade occurred), there is no significant

difference in phytoplankton dependent on the presence or absence of the river in the model – the

dominant control appears to be something else, surmised to be extreme mixed layer depth

123

generated by storm wind turbulence. December 2008 (lacking significant river discharge) has

little difference between the fully coupled model and the no-river control, except for an up to 1

degree Celsius drift in temperature, which oscillates in either direction over the course of the

month. This calls the meaningfulness of the temperature differences in 2003 and 2005 into

question, while simultaneously indicating that temperature is not the driver of differences in

phytoplankton growth between the fully coupled model and the no-river control. Finally, a

small bloom present in the MODIS data at the end of 2008, coincident with the first meaningful

discharge event of the water year, is wholly absent in the model. Whether this absence is due to

a failure to capture river dynamics in sufficient detail, or for another reason, is unclear.

124

3.5 Event-driven comparison

To more closely consider the presence and absence of the river in this system, we consider the

largest discharge events of each water year. Table 3.9 summarizes conditions during these

events from 2002-2010. Note the systematic underestimation of these storm discharge events by

HydroTrend, typically by a factor of two. HydroTrend is likely overestimating sediment by the

same amount, leading to a roughly accurate estimate then used in the model’s estimate of

particulate organic nitrogen (see Chapter 2.6.4). However, this insufficient discharge

undoubtedly had large physical effects on the modeled plumes, which likely were able to travel

over wider areas before losing their form in reality.

Table 3.9: Summary of conditions near the Eel River mouth during the largest discharge event of

each water year. Maxima and minima have been highlighted. Discharge from USGS gauging

station @ Scotia (USGS 2012). Precipitation and surface stress from the ERA-Interim

Reanalysis (Dee et al. 2011). Sea surface temperature is a model result.

Date Mean daily

discharge

(m3s): USGS

(left) and

HydroTrend

(right)

Mean sea

surface

temperature

(Celsius)

Daily

precip.

(inches)

Consecutive

days of

extreme

precipitation

Mean

surface

zonal stress

(N/m2)

Mean surface

meridional

stress (N/m2)

12/16/2002 4899 3816 10.3 1.63 8 0.02 0.4

2/18/2004 4899 2609 10 0.45 6 0.04 0.04

5/19/2005 2172 1165 11.5 0.04 6 0.06 0.05

12/31/2005 7447 3369 10.2 0.53 8 -0.02 0.3

12/27/2006 1696 2637 9.2 0.13 7 0.04 -0.04

1/5/2008 2679 2072 10 0.41 3 0.005 0.3

3/3/2009 1583 1158 9.6 0.5 3 -0.03 0.25

1/26/2010 2282 1880 9.5 0.06 11 -0.04 0.1

A wide variety of conditions are present across these nine water years. In the 2002, 2005 and

2008 water years, onshore stratification in the model has broken down leading to a relatively

deep mixed layer, over 100m in all cases. In the 2003, 2004, 2006 and 2009 water years, the

water column is much more stratified, and the mixed layer shallow. 2007 lies somewhere in

between these two extremes. This is a good first order separation with which to examine events;

the second separation is then between the size of river events, since 2008's largest event is five

times smaller than 2005's. That gives us four categories, summarized in Table 3.10:

Table 3.10: Categorization of oceanic conditions and relative strength of the largest Eel River

discharge event (as Table 3.9) of each water year. Mixed Layer Depth is a model result.

Water Year Large River Event Small River Event

Deep Mixed Layer 2002, 2005 2006, 2008

Shallow Mixed Layer 2003 2004, 2007, 2009

125

Across all events, despite varying seasons, weather conditions, mixed layer depths, and discharge

magnitudes, there is one consistent behavior that defines the Eel River’s apparent effect on

coastal ocean productivity in this modeling framework: during the largest discharge event of

each year, in plume-dominated portions of the water column, there is always simultaneously less

phytoplankton and less nitrate than in the no-river control (for a typical example, see Figure

3.14). This is an important result: given that phytoplankton take up nitrate as they grow, the

expected result would be to have less available nitrate in the system that has more phytoplankton.

For the no-river control to have more phytoplankton and more nitrate at the same time, compared

to the same regions under the influence of the plume, implies that the low-nitrate Eel River

plume creates nitrate limitation which inhibits phytoplankton growth compared to what could

have grown in ambient, comparably nitrate-rich ocean conditions untouched by the river.

Detritus, the slowly bioavailable biogeochemical tracer, is dominated by phytoplankton growth

and mortality rather than riverine delivery, which despite its extremely high estimated quantity

(described in Chapter 2), has no visible impact; if riverine detritus is enhancing phytoplankton

growth, its effect is heavily outweighed by other considerations (such as nitrate depletion).

This biogeochemical effect occurs under all conditions, but there are different physical plume

behaviors observed from year to year. Their overall importance on phytoplankton productivity is

outweighed by plume nitrate depletion, but they are still of interest. Model skill also varies,

providing insight into ways that the model is failing. This are summarized below, by category.

To avoid an overwhelming number of figures, only one event in each category is shown.

126

3.5.1 Large River, Deep Mixed Layer:

The modeled events in 2002 (not shown) and 2005 (Figure 3.14) both have reasonable model

skill at reproducing MODIS results (though as usual the presence of the model artifact makes

overall regression values low at best; see Table 3.11). These events were generated by long and

extreme storms, creating a deep mixed layer and a great deal of riverine discharge (shown in

Table 3.9). Their water columns (at the typical station described in section 3.4.3) have nearly

identical thermoclines (at 300m) and pycnoclines (starting at 200m onshore, rising to 100m by

ten kilometers offshore). Phytoplankton grow at a roughly constant and low rate, creating a low

concentration throughout the water column onshore. This follows the pycnocline, rather than the

thermocline, offshore, with a similar depth of about 100m. As is expected, detritus is enhanced

by mortality, while nitrate is depleted by growth, within the phytoplankton blooms.

However, there is a notable physical distinction between the two years; in 2002, the region of

plume-lowered salinity descends to 150m and is very diffuse, accompanied by a relative

warming of that region of the ocean. In 2005, the low-salinity, warmer region is four times more

concentrated, and sinks only to an absolute maximum of 100m onshore, shallowing to 50m

offshore. Examination of the conditions of each of these two years provides a reasonable

explanation: 2002 is the interannual maxima in both precipitation (with 300% of the precipitation

on the day of 2005’s event) and meridional surface stress (30% more in 2002 than in 2005). In

other words, 2002’s discharge event occurs during storm conditions of greater intensity, and is

mixed into the water column more thoroughly, accordingly. Additionally, 2005 delivers 150%

of the freshwater discharge of 2002, increasing the potential for a buoyancy-driven plume to

resist turbulent mixing for more of the 8-day average: it is thus much more visible.

Table 3.11: Pattern cross-correlation (R) values and normalized standard deviations for the 8-day

averages around 2002 and 2005 events, comparing the model results with to MODIS data.

Date and Model R Normalized standard

deviation

2002, day 345, w/river 0.158 0.6960784314

2002, day 345, w/o river -0.211 0.7107843137

2005, day 361, w/river 0.18 2.875

2005, day 361, w/o river 0.22 2.75

127

Figure 3.14: 8-day average starting at 12/31/2005, the highest Eel River discharge day in the

2005-2006 water year. A: ROMS phytoplankton. B: MODIS phytoplankton. C: ROMS results

minus the no-river control model results for phytoplankton. D, E, F: ROMS phytoplankton,

detritus, and nitrate respectively, at a 40.64 vertical transect (5 km north of the Eel River mouth)

out to 124.45 W. G, H, I: As D, E, F, with the no-river control subtracted from the results. J, K:

ROMS salinity and temperature along the same vertical transect. L, M: As J and K, with the no-

river control subtracted from the results.

128

3.5.2 Small River, Deep Mixed Layer:

2006 (Figure 3.15) and 2008 (not shown) comprise the entries in this category. Both are

extremely small river discharge events; 2008 is the smallest of all in the 2002-2009 water year

period, occurring after one of the shortest storms. 2006 has the coldest sea surface temperature

(with 2008 not far behind), and enjoys the outlier and minima of mean surface meridional stress;

the winds are blowing very weakly southward on average, unusual for a December storm event.

2008 has the typical strong northblowing winds of a winter storm event, yet occurs in March,

very late in the season.

The low calculated model chlorophyll-a (in 2006) compares well to MODIS data (particularly

near the river); 2008 does not compare well, as it includes the presence of a 4 mg chla/m3 bloom

all along the modeled coast that is largely not present in the satellite data. This behavior is

essentially dominated by the climatological differences discussed in section 3.3, and appears in

the differences in normalized standard deviation in Table 3.12; the 2008 modeled bloom not

present in MODIS creates great variability, while the 2006 results are roughly accurate in

variance, but spatially offset because of the southern model artifact (creating a negative R). In

both cases, however, we see the same interesting physical effect: the plume, though far less

massive than in 2002 or 2005, is highly concentrated and highly stratified within the water

column, essentially floating across the top. The phytoplankton is similarly concentrated at the

surface, markedly different from conditions in 2002/2005. Essentially what has happened is that

a freshwater plume has entered the ocean during well-mixed but now-calm conditions, and it

simply floats on the top, trapping the phytoplankton within a roughly 20m surface layer, where

they proceed to grow. Without the presence of the river, the phytoplankton mix more deeply into

the water column, but still enjoy more net productivity due to the greater available nitrate. The

thermal profile is the opposite of 2002/2005, with the upper region cooler rather than warmer

compared to the no-river control; given problems with thermal drift between the fully coupled

model and the no-river control (first discussed in 3.3.3 and explored more thoroughly in 3.8), it is

difficult to discuss the significance of this, as the magnitude of difference is near the noise

threshold defined later in Section 3.9.


averages around 2006 and 2008 (water year; 2008’s event falls in early 2009) events, comparing

the model results with and without the river with MODIS data.


deviation

2009, day 57, w/river -0.16 3.44

2009, day 57, w/o river -0.1 4.08

2006, day 361, w/river -0.38 0.8307692308

2006, day 361, w/o river -0.12 1.0769230769

129

Figure 3.15: As Figure 3.14, for the 8-day average starting at 12/27/2006, the highest Eel River

discharge day in the 2006-2007 water year.

130

3.5.3 Large River, Shallow Mixed Layer

Turning to the years of stratified water column, 2003 (Figure 3.16) has a river event of identical

strength as the well-mixed 2002 (whereas the rest of the Shallow Mixed Layer events are,

unsurprisingly, years with relatively minor storm events). What has changed between 2002/2005

and 2003 is the timing: it is now February instead of December. As it is February, the surface

fields are fairly different (we know from the section 3.3 climatologies that the model

overestimates blooms in February), with low R values. The general location of the bloom (as

seen in Figure 3.16) is very roughly correct, however, north of the cape – only with the bloom

considerably further offshore than in MODIS. February’s storm event also has an order of

magnitude less meridional stress than December 2002/2005 (see Table 3.13) providing turbulent

mixing. The pycnocline, in particular, is quite shallow, with an absolute maximum depth of

100m (whereas in 2002 and 2005 it tended to be twice as deep onshore). Phytoplankton grow

strictly above the pycnocline, trapped in that surface layer, with an according increase in detritus

and depletion of nitrate. The effect of the river is, in turn, trapped within the same layer, with the

same decrease in salinity that we see in 2005. The thermal effect is less consistent, and once

again at that level of low significance compared to thermal drift from the no-river control.

The effect of the river on the phytoplankton depth profile is fascinating. The no-river control has

up to 30% more growth in the top 20m; then, with the river present, this is reversed down to

100m depth. In other words: without the river, the phytoplankton concentrate much more closely

to the surface. With the river present, they seem to mix down throughout the pycnocline more

thoroughly. The differences in detritus follow this pattern, but nitrate, notably, does not: as

usual, there is relatively more nitrate throughout the no-river pycnocline, implicating the nitrate-

depleted freshwater as a relative suppressant of activity. Unlike in December, however, in

February there is enough nitrate present in the water column for the with-river phytoplankton to

grow anyway -- but not as effectively onshore at the surface, where the cooler river water

appears to inhibit growth.


averages around the 2003 (water year; the event occurs in early 2004) event, comparing the

model results with and without the river with MODIS data.


deviation

2004, day 49, w/river 0.06 2.12

2004, day 49, w/o river -0.1 2.55

131



132

3.5.4 Small River, Shallow Mixed Layer

This category is comprised of the drought years where storm (and river) events were small, and

the ocean tended to be warm and well-stratified, and so we see a wide degree of variability

within it: maximum river events ranging in timing from December to May, entering an ocean

with an equally variable state as defined by the season. The event in 2007 (Figure 3.17) occurs

at the beginning of January, and is thus directly comparable in season to most of the other events.

2007 has the typical southerly meridional stress of winter storm events, but the river event

occurred after a very short storm. 2007 has a notably shallow pycnocline of only 80m, which

phytoplankton follows. The river clearly contributes an apparently deepening layer of relatively

fresh water as it proceeds offshore, but it is small enough in magnitude that the thermal effects of

this especially cold plume (7.9 degrees Celsius, January plumes modeled as two degrees cooler

than the December plumes) are not significant.

When discussing the biogeochemistry of this system it’s important to start by noting that,

correctly reproduced by the model, very little phytoplankton is growing; all magnitudes are

small. Still, phytoplankton is clearly suppressed within the low-salinity surface plume. The

nitrate profile, unusually, has more nitrate in the with-river model than the no-river control

(though only outside of the plume); the small quantity of phytoplankton likely accounts for this

difference in behavior, as even at their most distinct, the with-river model and no-river control

have less than 1 mg chla/m3. The reason for this net positive nitrate is otherwise unclear; it is

unique among the events in all four categories, including the other small river, shallow mixed

layer events.

As usual, the southern model artifact creates small-to-negative negative R values. In the case of

2007, the very small values within the model create enormous normalized standard deviations,

since the artifact’s bloom (unreproduced by MODIS), while modest in concentration, is still

orders of magnitude more than what’s present in the satellite data. 2005’s variances are of the

same span as MODIS, though this tiny river event occurred during upwelling season and is

essentially drowned out by it, while the January 2010 event has similarly small values (and a

large, artifact-driven normalized standard deviation).


averages around the 2004, 2007 and 2009 (water year; all events occur in winter-spring of the

following year) event, comparing the model results with and without the river with MODIS data.


deviation

2005, day 137, w/river 0.18 0.96

2005, day 137, w/o river 0.11 1.08

2008, day 1, w/river -0.1 6.4

2008, day 1, w/o river -0.02 5.4

2010, day 25, w/river 0.08 3.11

2010, day 25, w/o river 0.13 2.91

133



134

3.5.5 Summary of event-driven comparisons

Across all of the largest discharge events in water years 2002-2009, regions of the water column

heavily influenced by the freshwater plume (as visualized by the difference in pycnoclines

between the fully coupled model and the no-river control) are universally nitrate limited as

compared to the no-river control. This effect dominates biogeochemistry in the system, above

any physical differences. Still, plume physical behavior varies widely; when entering an

especially deep mixed layer in the midst of an ongoing, surface stressful storm, it is often rapidly

mixed and heavily diluted by the time it reaches 5 km north over the course of eight days, though

larger deliveries of freshwater can resist this to some degree with buoyancy. If weather

conditions are calm, plumes can remain on top of the water column for several kilometers no

matter how deep or shallow the water column may be, nor how relatively massive or tiny the

plume. Plume-dominated regions are often warmer, but not consistently, and not significantly.

3.6 No-nutrient river testing

2005-2006, with the largest discharge event of the decade, was also selected to study the effects

of the river's nutrient load in greater depth, by running a separate experiment: rather than the no-

river control which lacks the river entirely, the no-nutrient control includes a physically identical

river with nitrate and detritus concentrations set to zero. By subtracting the no-nutrient control

from the with-nutrient river results, we can gauge how much of the river's effect within the

model is physical rather than due to biogeochemical loading. Given the model’s failure to

precisely reproduce the spatial distribution of the coastal bloom, the application of this analysis

to reality must be considered with some care.

In section 3.5 it became clear that in terms of nitrate contribution, the river functionally creates a

region of nitrate deficiency due to its relatively low concentration (based on USGS data, USGS

2012) compared to the surrounding ocean (based on the World Ocean Atlas, NOAA 2013c).

Detritus, however, is delivered by the river to the ocean in considerably higher quantities

(described in Chaper 2.6.4), which can be remineralized by phytoplankton and used to grow.

Despite this, at no point throughout the December-May season of river discharge was

productivity enhanced by more than 4% in the with-nutrient river runs as compared to the

control. The best example of this behavior occurs immediately after the river discharge event at

the beginning of February 2006. Figures 3.18 to 3.20 show the region of elevated, nutrient-

driven productivity. This productivity is small, of the same order of magnitude as inherent

indeterminacy between the two models, but its timing (after a large river event) and location

(near the mouth of the river) allow us to reasonably interpret it as dominated by the

biogeochemical difference between the experiments rather than the numerics. Furthermore,

throughout sections 3.4 and 3.5, the sign of the difference of detritus between models with and

without the river was always determined by the sign of the difference in phytoplankton

concentration; riverine-delivered detritus was overwhelmed by ongoing biological cycling. In

summary, these results indicate that river-delivered nitrate (whether initially dissolved or later

bioavailable through remineralization of detritus) is unimportant to the phytoplankton that grow

around Cape Mendocino. It is of course, possible that a different nutrient, such as iron, would

show much more interesting results. It is also possible that a mechanistic failure of the model is

obscuring nitrate’s true importance, such as an inability on the part of the phytoplankton to

135

uptake it to full depletion, or too much nitrate delivered in the first place during the model spin-

up period.

Figure 3.18: 8-day averaged phytoplankton results from the no-nutrient river control subtracted

from the with-nutrient river, beginning 02/02/2006, which is also the time of delivery of the

second-largest river discharge event of the water year. Note that ambient phytoplankton

concentration at the mouth of the Eel River is 1.5 mg chl-a/m3, such that this difference accounts

for no more than 4% of the total.

136

137


from the with-nutrient river, beginning 02/09/2006. Note that ambient phytoplankton

concentration at the mouth of the Eel River is 0.5 mg chl-a/m3, such that this difference

accounts, as in Figure 3.18, for no more than 4% of the total.

138


from the with-nutrient river, beginning 02/17/2006. Note that ambient phytoplankton

concentration at the mouth of the Eel River is 0.5 mg chl-a/m3, such that this difference

accounts, as in Figures 3.18-.3.19, for no more than 4% of the total.

139

3.7 Extra-nutrient river testing

While the lack of significance of riverine nutrient delivery is not improbable, it spurred the

question of whether or not the modeling framework was capable of successfully modeling

riverine nutrient-driven phytoplankton blooms at all. To test the model’s capability in doing so,

the Eel River was loaded with four hundred times its usual concentration of nitrate (roughly

equaling the annual nitrate load of the Seine River, estimated at 80,000t by (Guillaud et al.

2000)). For comparison, the Columbia River’s annual nitrate load is estimated at 50,000t

(Aulenbach 2006), and the Mississippi River’s can approach 1,000,000t (Aulenbach 2006), while

the Amazon River is estimated to annually export over 1,300,000t (DeMaster and Aller 2001).

As Figure 3.21 shows, with that level of nitrate delivery, even in the lowest-flow months of the

year, like July, a phytoplankton bloom can easily be sustained. It is therefore not the inability of

the model to resolve river nutrient delivery to the coastal biogeochemical system at work here,

but rather the relatively low quantity of nutrients being delivered, that accounts for the model’s

lack of response in earlier sections.

140

Figure 3.21: A large phytoplankton bloom generated by the coupled modeling framework during

low-flow conditions in July, with the Eel River given 400x its normal load of dissolved inorganic

nitrogen.

141

3.8 Chl:C sensitivity testing

As discussed in section 2.6.3, the Carbon:Chlorophyll ratio is a potential additional source of

model uncertainty. It varies greatly by species and is affected nonlinearly by ambient nutrient,

light, and temperatures (Wang et al. 2009). Its primary potential to alter model results is in

defining the values for initialization of the model. In order to test the potential impact of an

inaccurate constant ratio (50 C:Chl, per Li et al. [2010]), the 2005-2006 model year was spun up

with ten times more initial phytoplankton. The effect was magnified on the southern boundary in

the problematic region discussed in 3.8, but in terms of onshore results in the region of interest,

the additional initial phytoplankton influenced results by no more than 0.1 mg chl-a/m3 by the

end of the spin-up period in November.

3.9 Southwestern model artifact and nonlinear drift

The major failure of the modeling framework’s ability to reproduce realistic coastal

phytoplankton conditions clearly occurs to the southwest (for example, in Figure 3.3, the

November-January climatologies); it routinely overestimates primary production by

approximately a factor of two. This artifact is so dominant south of Cape Mendocino that it

makes it difficult to interpret model results there. It is fortunate that the river is literally shielded

from the worst of the artifact’s impact by virtue of being further north.

The source of this model artifact is easy to find: open boundary conditions in ROMS are

notoriously unstable, and the southern boundary in this model application exemplifies that

behavior. Due to concerns about computational expense, 39 N was chosen as the southern extent

of the 1 km domain, but this is clearly not far enough away from the region of interest – results

would be improved by moving the southern boundary down another – probably several –

hundred kilometers. Instability from the southern boundary is the likely driver of most of the

otherwise inexplicable difference between models with and without the river – when there are

significant differences between the model and the control two hundred kilometers offshore, it’s

unlikely that the lack of a river is the primary actor when comparing the two.

This boundary-driven artifact then interacts with the other major failure of model skill: the

Mendocino Triple Junction, where the Gorda plate, the North American plate, and the Pacific

Plate meet, is at 40.36 N, -124.6 W – in other words, just south of Cape Mendocino. Even

smoothed to some degree in the model, this creates a change in bathymetry of 1000-1500m over

10 km (and thus ten grid cells). Resolving momentum over this region is a challenge. In the

case of these results, what reliably occurs is the creation of an unrealistic vortex in the

southeastern corner of the model (for a typical example, see Figure 3.22), which is clearly

partially driven by the proximity of the southern boundary as well, and could be reduced in the

same fashion. This rotating water draws anything nearby into itself – particularly, it transports

the boundary-instability generated phytoplankton into itself, concentrating this nonphysical

bloom right where it’s visible in so many figures in this chapter, west and south of Cape

Mendocino. In a way this artifact vortex is fortuitous; it cooperates with the presence of Cape

Mendocino to draw the effects of the southern boundary away from the small and usually

northern region potentially dominated by the river at certain times of year.

142

Figure 3.22: 11/25/05 example of the model artifact vortex created by momentum over the

Mendocino Triple Junction, and further interactions with the unstable southern boundary.

143

That isn’t to say that this problem would evaporate with the further distancing of the southern

noise, however. In a nonlinear modeling framework, nonlinearities can amplify fluctuations in

unpredictable fashion – and while the steady addition of fresh water during the low-flow months

of spinup is not large in mass, it is certainly a continuous perturbation. Differences accumulate,

both from the addition of the freshwater, and from the closed boundary in the no-river control

replacing the river’s mouth, where the ocean is forced to stop at the shore instead of mixing

slightly inland. Some of these differences are potentially quite physically meaningful; the

purpose of “turning off” the river, after all, is to explore all of the potential impacts of the river,

and the altered boundary captures that! But others may well simply be nonlinear drift, as tiny

differences accumulate during spinup, and the solutions diverge in potentially significant ways.

Trying to quantify this drift is both more difficult and more necessary than the southwestern

boundary artifact because its effect is by definition concentrated near the river. A first order

consideration, made regularly in previous analysis in this chapter, is that an order of magnitude

estimate of inherent model differences can by estimated from the differences between the with-

river model and no-river control that accumulate before the first major river discharge event.

Differences significantly larger than that initial difference, during storm-driven river discharge

events, are more likely to be event-driven than caused by longer-term effects, whether numerical

or physical). The differences between the November climatologies with and without the river –

November being the sole post-spinup, pre-storm event month modeled each year – provide a

more systematic definition of this uncertainty.

Table 3.15: The absolute magnitudes of November minus No River November climatological

results within 10 km of the mouth of the Eel River.

Nitrate

(mmol/m3)

Detritus

(mmol/m3)

Phytoplankton

(mmol/m3)

Zooplankton

(mmol/m3)

Temperature

(deg. C)

Salinity

(psu)

U

velocity

(m/s)

V

velocity

(m/s)

1 0.08 0.05 0.02 0.3 0.5 0.02 0.02

Compared to most of the model-control differences we see during large storm events, the

biological tracer differences are especially minute, and the differences in momentum are also

small, but salinity and temperature differences often fall within the same order of magnitude as

the post-spinup drift in Table 3.15. That is not to say that the warm, low-salinity regions

reproduced over and over in the right place at the right times are meaningless; their true

magnitude, however, may up to a factor of two larger, or considerably smaller, depending on the

(unknown) sign of the background noise.

3.10 Discussion

Although high levels of noise make it challenging to interpret the effect of the modeled Eel

River, a few broad conclusions can be drawn. In the months of highest river activity, December

and January, large discharge events usually have an inhibitory effect on phytoplankton growth,

on time scales ranging from interannually, to monthly, to weekly. The delivery of an extreme

amount of river water is generated by storm events: these storm events deepen the mixed layer,

reducing light availability (and phytoplankton growth). While structured river plumes are

144

observed within the model at a distance of 5 km north of the mouth, the potential buoyancy-

driven shallowing effect of freshwater delivery is often overcome by mixing, instead creating a

region of lower salinity that is spread more evenly above the pycnocline. Onshore, the

pycnocline is consistently shallower than the thermocline by at least 100m, and the

phytoplankton grow above it.

Within this region, there are clear indications of nutrient limitation: the natural outcome of

phytoplankton growth is to deplete dissolved inorganic nitrogen, but the no-river control

consistently has simultaneously more phytoplankton and more nitrate than the with-river model.

In other words, the lack of nitrate within the plume-dominated system is so dominating that even

when phytoplankton grow to greater magnitudes in the riverless ocean, they still leave more

nitrate behind than is available during periods of high river discharge!

There does seem to be the possibility of second-order thermal effects, but they are difficult to

separate from the noise. The low-salinity water often appears to be slightly warmer, probably

due to the elevated heat capacity compared to the surrounding ocean. This can come with a

corresponding increase in phytoplankton concentration, but only when (as for example in

December 2003) the mixed layer is shallow. At the moment that it enters the system, the

December and especially January river is colder than the ocean, but the effect of that initial

temperature is drowned out by the current ocean/atmosphere conditions: it can float, sink, or be

mixed in evenly, irrespective of initial temperature.

It is when the river enters an ocean with a shallow mixed layer that light limitation appears to

play a role; the difference in nitrate between the with-river model and the no-river control gets

smaller, and the depth profile of the phytoplankton strongly favors the surface rather than being

mixed more evenly throughout the mixed layer. Supported by a shallower mixed layer (and less

turbulence), the low-salinity region of river influence is itself shallower, and sometimes

distinctly above the pycnocline, forming its own layer on the surface. In other words, if the

storm event that generates a river event clears up quickly enough that the ocean can calm down a

bit, river plumes appear to have a chance to propagate without being as rapidly mixed into the

water column.

A great degree of mixing by the time the plume reaches the vertical transect station at 5 km north

of the mouth is not unexpected. The physical anatomy of a river plume is still a subject of active

research, but a typical model involves rapid shear mixing and entrainment of ocean water, thus

increasing the salinity, in the near-field, advective region; as the plume moves away from the

mouth of the river, this far-field region becomes dominated by wind stress (Hetland 2005). It is

the far-field, rather than the near-field, that is under examination (as the near-field at the mouth is

acted on by freshwater year round, and while it is dynamically event-driven, it is that much more

difficult to separate those events from the background). The basic mechanism was described by

Fong and Geyer (2001): a buoyant layer is mixed by shear created by the wind-driven Ekman

transport. The predicted result is a critical salinity value, derived from initial conditions, wind

stress, and the Richardson number, that causes wind mixing to stabilize the water mass structure

of the plume (whatever state it’s in, after its initial near-field inertial mixing) towards that

salinity value. This is consistent with our model’s behavior; in the far-field, most of the mixing

has already occurred, and what we see is often relatively diffuse.

145

Given the model's tendency to overestimate phytoplankton production, the occasional

underestimated bloom event is of particular interest. For example, the failure of the 2008 model

to generate a bloom at the end of December, coinciding with the year's first river delivery event,

implies a mechanistic failure. It could be due to differences between the atmospheric

representation and reality, but it could also be due to effects not accounted for in the model. If

the river does play a role in the generation of that bloom, it is a particularly good time for

nutrients to be meaningful -- with the first storm event/river delivery of the year most likely to

carry a load of nutrients leeched from the ground Perhaps an alternative micronutrient, like iron,

is important..

Using gradually remineralizable-to-nitrate detritus as a stand-in for a more detailed treatment of

non-DIN nutrients is not an effective way to gauge this possibility. Especially problematic, the

effect of river-added detritus, even at high levels, was totally overwhelmed by the detritus

produced by plankton grazing and mortality. When comparing detritus with and without the

river, it followed the difference in phytoplankton very consistently, which usually meant more

detritus without the river than with it. There was no evidence that the river-delivered detritus

was sinking out of the water column before it could be remineralized, so its overall effect on the

system seems to be extremely minor. Zooplankton, the last piece of the NPZD puzzle, have

gone largely unmentioned throughout the chapter because they behaved extremely predictably,

maintaining populations roughly proportional to the phytoplankton throughout.

Something else not considered by the model is variable turbidity; the exponential decay of light

through the water column is potentially much hastened by suspended sediment absorbing the

light. This must account for some degree of model overestimation in near-mouth regions where

the sediment has not yet left the euphotic zone, since its net effect would always be to inhibit

growth whenever light limitation is a factor.

146

3.11 Future Directions

In the immediate term, reconfiguring the model with the boundaries further away from the region

of interest would probably have the single largest impact on model skill. Beyond that, though,

there are many interesting directions in which to take the model.

The use of an iron-limited NPZD model such as Fiechter et al. (2009) is a straightforward way to

add iron to the system. Its major limitation in application to this effort is that this model

continuously recharges shelf iron at a constant rate, on the assumption of riverine delivery; a

model configured to study the specifics of riverine delivery would need to replace this

framework with a more detailed structure. Chase et al. (2007) proposes a framework in which

riverine iron must sink to anoxic depths, transform from ferric to the more soluble ferrous state,

and be upwelled before biological uptake. Iron reduction and oxidation kinetics within the ocean

are not so well understood that directly modeling their reactive transport would be reasonable,

but there are first-order approximations to be made. Treating iron as a tracer with a delayed

release, such that it only dissolves at a certain depth after a certain time (or at a certain oxygen

content, if oxygen is modeled directly) is one possible strategy. Bioavailability as a function of

the iron-scavenging ligand production by phytoplankton (Buck et al. 2007) is another mechanism

for iron uptake that could be modeled directly.

Additionally, river sediment could be modeled directly (at great computational expense, if it

were done with significant detail); some kind of tracer to represent turbidity, at the least, would

add a potentially important piece to the model, while the sediment itself could provide more

accurate representations of gradually bioavailable iron and nitrogen than 'detritus', which is

constant in assumed size and sinking rate. Another constant that should be variable is the

Carbon:Chlorophyll ratio. Although the model's sensitivity to this value was not shown to be

large, an improved representation would help most at the validation stage; converting carbon to

chlorophyll at any given moment to compare to MODIS (or other chlorophyll) results

necessitates something of a leap of faith when using a constant. The true C:Chl ratio could easily

be a factor of two different, depending on current environmental conditions. Gruber et al. (2006)

is one example of an attempt to nest C:Chl dynamics into ROMS, and could be emulated.

Although they found that while large horizontal and vertical variations in the ratio were present,

they tended to cancel out within the integrated mean across the euphotic zone, they also showed

that using a constant would have created a very substantial negative bias in their model, in

contrast to model results in this work.

On a larger scale, there is interest in incorporating watershed models into global climate models

such as the Community Earth System Model (CESM). Such problems as tracking sediment and

nutrient transport from rivers to the ocean are currently largely unimplemented in comprehensive

global climate models. Successful coupling on the mesoscale is an important first step in model

development. The hindcast modeling framework could be forced forward with CESM results to

explore decadal-scale variability under a variety of climate change emissions scenarios.

Eventually the framework could even be implemented as an option within CESM, using its land

parameterizations to automatically parameterize a nested HydroTrend or (more likely, given

HydroTrend’s limitations) another sufficiently simple watershed model.

147

3.12 Conclusion

The coupled modeling framework is a powerful tool to examine potential effects by the Eel

River on coastal ocean productivity. In the current formulation, nitrogen limitation in freshwater

plumes appears to be a major factor in the biogeochemical response to their offshore delivery.

Typically, the same storm events that generate large plumes also create turbulence that deepens

the mixed layer, inhibiting phytoplankton production. On 8-day timescales, storm wind-driven

mixing appears to create relatively diffuse plume conditions by the time the plume is 5 km north.

Occasionally, however, conditions clear up rapidly enough to allow an especially low-salinity

plume to travel across the surface for tens of kilometers, trapping phytoplankton closer to the

surface. Even under these conditions, nutrient limitation appears to inhibit production, however.

The effect of gradually remineralizable detritus delivered by the river appears to be negligible,

even given the very high upper bound chosen.

Potential improvements to the modeling framework range from the expansion of the model

domain to diminish unstable boundary noise, to the inclusion of iron limitation or the direct

simulation of turbidity caused by sediment load. Although it was run as a nine-year hindcast,

there is also potential to force the framework forward with climate projections, in order to learn

how the altered timing and magnitude of storm events might change the subsequent behavior of

the river entering the coastal ocean. Although the impact of the river on ocean productivity

appears to be small on short time scales, it is possible that the incremental shift of phytoplankton

bloom locations might alter longer-term dynamics, such as nutrient availability during upwelling,

later in the year.

148

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